HOUSTON JOURNAL OF
MATHEMATICS

Electronic Edition Vol. 38, No. 4 , 2012

Editors: G. Auchmuty (Houston), D. Bao (San Francisco, SFSU), D. Blecher (Houston), H. Brezis (Paris and Rutgers), B.  Dacorogna (Lausanne), K. Davidson (Waterloo), M. Dugas (Baylor), M. Gehrke (LIAFA, Paris7), C. Hagopian (Sacramento), R. M. Hardt (Rice), Y. Hattori (Matsue, Shimane), J. A. Johnson (Houston), W. B. Johnson (College Station),  V. I. Paulsen (Houston), M. Rojas (College Station), Min Ru (Houston), S.W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)

Houston Journal of Mathematics


Contents

Keef, Patrick, Whitman College, Walla Walla, WA 99362 (keef@whitman.edu),  and Danchev, Peter, Dept. of Mathematics, Plovdiv University ``P. Hilendarski'', Plovdiv 4000, Bulgaria (pvdanchev@yahoo.com).
On n-simply presented primary abelian groups, pp. 1027-1050.
ABSTRACT. Two natural classes of exact sequences of primary abelian groups are defined that generalize the balanced-exact sequences and another important class of sequences studied by Nunke. These classes have enough projectives, which are described in relation to the simply presented groups. Important results on simply presented groups and totally projective groups are generalized to this new framework.

Chung, Weonil, Hoseo University, Asan 336-795, Korea, Ha, Jaecheol, Hoseo University, Asan 336-795, Korea, and Kim, Hwankoo, Hoseo University, Asan 336-795, Korea (hkkim@hoseo.edu).
Some remarks on strong Mori domains, pp. 1051-1059.
ABSTRACT. We show that for an extension T of an integral domain R such that T is a w-finite type R-module, if R is a strong Mori domain, then so is T; and its converse, the Eakin-Nagata Theorem for strong Mori domains, holds true, provided an additional assumption on the extension. We also present a variant of Cohen's Theorem for strong Mori domains.

Koubek, V., Charles University, 11800 Praha, Czech Republic (koubek@ktiml.mff.cuni.cz), and Sichler, J., University of Manitoba, Canada R3T2N2 (sichler@cc.umanitoba.ca).
Distributive (0,1)-lattices with an added constant, pp. 1061-1089.
ABSTRACT.Distributive (0,1)-lattices with an added nullary operation form a category that is relatively universal with respect to the ideal formed by all homomorphisms with finite image, and one containing arbitrarily large sets of non-isomorphic objects whose endomorphism monoids are isomorphic.

Rafael López, Departamento de Geometría y Topología Universidad de Granada 18071 Granada. Spain (rcamino@ugr.es).
Constant mean curvature surfaces in Sol\\ with non-empty boundary, pp. 1091-1105.
ABSTRACT. In homogenous space Sol we study compact surfaces with constant mean curvature and with non-empty boundary. We ask how the geometry of the boundary curve imposes restrictions over all possible configurations that the surface can adopt. We obtain a flux formula and we establish results that assert that, under some restrictions, the surface inherits the symmetry of its boundary.

Hladky, Robert, North Dakota State University, Fargo, ND, 58108 (robert.hladky@ndsu.edu).
Connections and curvature in sub-Riemannian geometry, pp. 1107-1134.
ABSTRACT.  For a sub-Riemannian manifold and a given Riemannian extension of the metric, we define a canonical global connection. This connection coincides with both the Levi-Civita connection on Riemannian manifolds and the Tanaka-Webster connection on strictly pseudoconvex CR manifolds. We define a notion of normality generalizing Tanaka's notion for CR manifolds to the sub-Riemannian case. Under the assumption of normality, we construct local frames that simplify computations in a manner analogous to Riemannian normal coordinates. We then use these frames to establish Bianchi Identities and symmetries for the associated curvatures. Finally we explore sub-Riemannian generalizations of the Bonnet-Myers theorem, providing some new results and some new proofs and interpretations of existing results.

Borel-Mathurin, Laetitia, Université Pierre et Marie Curie, Institut Mathématiques de Jussieu, Analyse Fonctionnelle, case 247, 4 place Jussieu, 75252 Paris Cedex 05, France (borel@math.jussieu.fr).
Approximation properties and non-linear geometry of Banach spaces, pp. 1135-1148.
ABSTRACT. The existence of Lipschitz quasiadditive projections on linear subspaces is investigated. A new charaterization of the bounded approximation property provides an alternative proof of the equivalence between this property and its Lipschitz version. We show that Lipschitz-free spaces over finite-dimensional normed spaces have a finite-dimensional decomposition.

Bès, Juan, P. and Martin, Özgür, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403 (jbes@bgsu.edu), (omartin@bgsu.edu).
Compositional disjoint hypercyclicity equals disjoint supercyclicity, pp. 1149-1163.
ABSTRACT. We show that for sequences of composition operators with automorphic symbol of a simply connected domain, compositional disjoint hypercyclicity equals disjoint supercyclicity.

You Qing Ji,Department of Mathematics, Jilin University, Changchun 130012, P.R. CHINA (jiyq@jlu.edu.cn), and Luo Yi Shi,Institute of Mathematics, Jilin University, Changchun 130012, P.R. CHINA (sluoyi@yahoo.cn).
Amenable operators on Hilbert spaces, pp. 1165-1183.
ABSTRACT. In this paper, we study the amenability of the closed subalgebra generated by an operator on complex separable infinite-dimensional Hilbert space. We show that if an operator is a normal operator plus a compact operator which commuting with the normal operator, then it is amenable if and only if it is similar to a normal operator whose spectrum has connected complement and empty interior; a polynomial compact operator is amenable if and only if it is similar to a normal operator whose spectrum has connected complement and empty interior; a finite type spectral operator is amenable or weakly amenable or character amenable if and only if it is similar to a normal operator whose spectrum has connected complement and empty interior.

Giol, Julien, RMC Saint-Jean Science Departement, Saint-Jean-sur-Richelieu QC JOJ 1RO, Canada (julien.giol@gmail.com).
Affine coordinates and finiteness, pp. 1185-1196.
ABSTRACT.We show that a von Neumann algebra is finite if and only if its Grassmannians are small in a certain sense related to the atlas of affine coordinates.

Boudi, Nadia, Faculté des Sciences, Université Moulay Ismail, BP 11201, Meknes, Morocco (nadia_boudi@hotmail.com), and Šemrl, Peter, University of Ljubljana, Jadranska 19, SI 1000 Ljubljana, Slovenia (peter semrl@fmf.uni-lj.si).
Semi-group automorphisms of nest algebras, pp. 1197-1206.
ABSTRACT.  We prove that every bijective multiplicative map acting on a nest algebra on an infinite-dimensional Banach space is a spatial linear or conjugate-linear automorphism.

Moreno, Jose Pedro, Dpto. de Matemáticas, Universidad Autónoma, Madrid 28049, Spain, (josepedro.moreno@uam.es), and Schneider, Rolf, Mathematisches Institut, Albert-Ludwigs-Universität, D-79104 Freiburg I. Br., Germany, (rolf.schneider@math.uni-freiburg.de).
Local Lipschitz continuity of the diametric completion mapping, pp. 1207-1223.
ABSTRACT. The diametric completion mapping associates with every closed bounded set C in a normed linear space the set of its completions, that is, of the diametrically complete sets containing C and having the same diameter. We prove local Lipschitz continuity of this set-valued mapping, with respect to two possible arguments: either as a function on the space of closed, bounded and convex sets, while the norm is fixed, or as a function on the space of equivalent norms, while the set C is fixed. In the first case, our result is valid in spaces with Jung constant less than 2, whereas the result in the second case is only proved for finite dimensional spaces. In this setting, we further show: (i) the maximal volume completion is a continuous selection for the diametric completion mapping if the space is strictly convex, (ii) the diametric completion mapping is convex valued if and only if the space has the property, studied by Eggleston, that every diametrically maximal set is of constant width.

Bingzhe Hou, Institute of Mathematics, Jilin University, Changchun 130012, P.R.China (houbz@jlu.edu.cn), Gongfu Liao, Institute of Mathematics, Jilin University, Changchun 130012, P.R.China (liaogf@email.jlu.edu.cn), Yang Cao, Institute of Mathematics, Jilin University, Changchun 130012, P.R.China (caoyang@jlu.edu.cn).
 Dynamics of shift operators, pp. 1225-1239.
ABSTRACT. IIn this article, some dynamical properties of unilateral backward weighed shift operators are considered. We obtain the complete classification for shift operators with constant weight in the sense of topologically conjugacy. Sensitivity and Li-Yorke chaos are also considered. We prove that they are equivalent for unilateral backward weighted shift operators. At the end, we show an interesting phenomenon: Every bounded orbit under a Devaney chaotic weighted shift operator is compact. However, there exists a bounded orbit with empty omega-limit set under a sensitive weighted shift operator.

Ionescu, Marius, Colgate University, Hamilton, N.Y. 13346 (mionescu@colgate.edu) and Williams, Dana P., Dartmouth College, Hanover, N.H. 03755 (dana.williams@dartmouth.edu)
Remarks on the ideal structure of fell bundle C*-algebras , pp. 1241-1260.
ABSTRACT. We show that if p : B → G is a Fell bundle over a locally compact groupoid G and that A=Γ0(G(0);B) is the C*-algebra sitting over G(0), then there is a continuous G-action on Prim(A) that reduces to the usual action when B comes from a dynamical system. As an application, we show that if I is a G-invariant ideal in A, then there is a short exact sequence of C*-algebras 0 → C*(G,BI) → C*(G,B) → C*(G,BI) → 0 where C*(G,B) is the Fell bundle C*-algebra and BI and BI are naturally defined Fell bundles corresponding to I and A/I, respectively. Of course this exact sequence reduces to the usual one for C*-dynamical systems.

L.P. Castro, Department of Mathematics and Center for R&D in Mathematics and Applications, University of Aveiro, 3810-193 Aveiro, Portugal (castro@ua.pt),  H. Itou, Department of Mathematics, Graduate School of Engineering, Gunma University, Kiryu 376-8515, Japan (h-itou@math.sci.gunma-u.ac.jp),  and S. Saitoh, Department of Mathematics and Center for R&D in Mathematics and Applications, University of Aveiro, 3810-193 Aveiro, Portugal (saburou.saitoh@gmail.com).
Numerical solutions of linear singular integral equations by means of Tikhonov regularization and reproducing kernels, pp. 1261-1276.
ABSTRACT. In this paper, a reproducing kernel method is proposed to perform the analysis of different types of singular integral equations. We will be mostly interested in linear singular integral equations of Cauchy type which have functions as coefficients (for which an equation of Carleman type serves as a model). Anyway, due to the nature of our method we will be also able to study corresponding so-called discrete singular integral equations and inverse source problems. All this include a new concept and method which provides practical and numerical solutions of very general linear singular integral equations by combining the two theories of Tikh

Ryle, J. and Trent, T. T., The University of Alabama, Tuscaloosa, AL 35487 (ttrent@as.ua.edu).
A corona theorem for certain subalgebras II, pp. 1277-1295.
ABSTRACT. We prove corona theorems with bounds for various subalgebras of bounded analytic functions on the unit disk.

Liang-Xue Peng, College of Applied Science, Beijing University of Technology, Beijing 100124, China (pengliangxue@bjut.edu.cn).
A note on transitively D and D-spaces, pp. 1297-1306.
ABSTRACT. D-spaces were introduced by van Douwen and Pfeffer in 1979 and studied by many topologists. In 2008, Peng developed the idea of D-spaces and introduced the notion of a transitively D-space. In this note, we mainly show that some spaces which have weaker covering properties are transitively D. We show that every weak θ-refinable space is transitively D . As a corollary, we have that meta-Lindelöf spaces and weak θ-refinable spaces are transitively D-spaces. Thus some known conclusions on transitively D and linearly D are generalized. In the second part of this note, we point out that transitively D, linearly D, aD, and D are equivalent in the class of GO spaces.

Włodzimierz J. Charatonik and Robert P. Roe, Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65401 (wjcharat@mst.edu), (rroe@mst.edu).  Inverse limits of continua having trivial shape, pp. 1307-1312.
ABSTRACT.We show that trivial shape is preserved under inverse limits of continua with multivalued bonding functions provided the images of points have trivial shape. Some examples are provided.

Charatonik, Włodzimierz J. and Matt Insall, Dept. of Mathematics and Statistics, Missouri University of Science and Technology, 400 W. 12th Street, Rolla, MO 65409-0020, (insall@mst.edu), (wjcharat@mst.edu)
Absolute differentiation in metric spaces, pp. 1313-1328.
ABSTRACT. In this article, we introduce a new notion of (strong) absolute derivative, for functions defined between metric spaces, and we investigate various properties and uses of this concept, especially regarding the geometry of abstract metric spaces carrying no other structure.

A. Bouziad, Département de Mathématiques, Université de Rouen, UMR CNRS 6085, Avenue de l'Université, BP.12, F76801 Saint-Étienne-du-Rouvray, France (ahmed.bouziad@univ-rouen.fr ), and M. Filali, Department of Mathematical Sciences, University of Oulu, P.O.Box 3000, 90014 Oulu, Finland (mahmoud.filali@oulu.fi ).
The Stone-Čech compactification of a topological group as a semigroup and the SIN property, pp. 1329-1341.
ABSTRACT. For a Hausdorff topological group G, we consider the Banach space Cb (G) of bounded, continuous, scalar-valued functions on G with the supremum norm, together with the subspace Clm (G) of left multiplicatively continuous functions and the subspace Cru (G) of right uniformly continuous functions. We prove that every uniformly normal group G is SIN. If the Stone-Cech compactification βG is a semigroup compactification with the joint continuity property then G is SIN. The first answers a question asked by Protasov and the second answers partially a question posed in a recent article co-authored by the second author. Moreover, when G is non-SIN, the quotient space Cb (G)/Cru (G) contains a linear isometric copy of l∞ . When G is not precompact and not a P-group, the quotient Cb (G)/Clm (G) contains a linear isometric copy of  l∞. In particular, both quotient spaces are non-separable. These results are improvements and extensions of theorems proved recently by the authors of this article and by O. T. Alas.

Aguilera, María Elena  Instituto de Matemáticas, Universidad Nacional Autónoma de Mexico, 04510, México, D.F. (aguilera@matem.unam.mx)  and Illanes Alejandro,  Instituto de Matemáticas, Universidad Nacional Autónoma de México, 04510, Mexico, D.F. (illanes@matem.unam.mx).
Connectedness properties of the hyperspaces Cε(X), pp. 1343-1354. ABSTRACT. For a metric continuum X and r > 0, let Cε(X) be the hyperspace of subcontinua of X of diameter less than or equal to r. In this paper we answer several questions posed by Eric L. McDowell and B. E. Wilder. We prove that if X is a metric continuum and r > 0, then: (a) if X is arcwise connected, then Cε(X) is cyclicly connected, (b) Cε(X) is not separated by any of its zero-dimensional subsets, and (c) Cε(X) is zero-dimensional closed set aposyndetic.

Alas, Ofelia T., Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, 05311-970 São Paulo, Brasil (alas@ime.usp.br), Sanchis, Manuel, Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec, 12071 Castelló, España (sanchis@mat.uji.es), and Wilson, Richard G., Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco 186, Apartado Postal 55-532, 09340, México, D.F., México (rgw@xanum.uam.mx).
Maximal pseudocompact and maximal R-closed spaces, pp. 1355-1367.
ABSTRACT. A space X is pseudocompact if it is Tychonoff and every real-valued continuous function on X is bounded and X is R-closed if it is closed in every embedding in a regular Hausdorff space. We obtain conditions under which a Tychonoff space is maximal pseudocompact and study conditions under which a regular space is maximal R-closed.

Sina Greenwood, Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand (sina@math.auckland.ac.nz) and Judy Kennedy, Department of Mathematics, Lamar University, Beaumont, TX 77710, USA, (kennedy9905@gmail.com).
Generic generalized inverse limits, pp. 1369-1384.
ABSTRACT.We show that generalized inverse limits formed from upper semicontinuous maps from an interval into the closed subsets of that interval are generically Cantor sets. Indeed, most such generalized inverse limits have upper semicontinuous maps whose graphs are pseudoarcs - we call them pseudoarc generalized inverse limits. All pseudoarc generalized inverse limits are totally disconnected, but they may contain isolated points. Furthermore, in the space of all generalized inverse limits in the Hilbert cube, those pseudoarc generalized inverse limits form a dense Gδ set. It follows that such generalized inverse limits are generic, and generic generalized inverse limits are Cantor sets.

Corrigendum of the paper "Generic generalized inverse limits" by Sina Greenwood and Judy Kennedy:
After acceptance in February 2012, the authors discovered a mistake and decided to retract the paper shortly afterwards. Because of several technical mishaps, the paper was published anyway. The statement that "generic generalized inverse limits are Cantor sets" seems to be wrong. What was proven is that "generic generalized inverse limits are hereditarily disconnected (i.e., no closed non-degenerate sub-generalized inverse limit is connected) with no isolated points.
Authors submitted correction: April 16, 2013. Posted: May 13, 2013.