Publications

Book:

  • Cover
  • Operator Algebras and Their Modules - An operator space approach", by David P. Blecher and Christian Le Merdy, Oxford University Press (2004). The book is available on www.amazon.com or at: http://www.oup.co.uk/isbn/0-19-852659-8

You may download Chapter 1 of this book at http://fdslive.oup.com/www.oup.com/academic/pdf/13/9780198526599.pdf

Many of the preprints below may be downloaded from the Los Alamos Preprint Server which may be accessed from the ArXiV site at https://arxiv.org (a couple are downloadable from links below). Be warned however that the version that appears there is not the final revised version (even if it says that it is) - see the journal for that. For a list of those which have already appeared, or for preprints, write me.
    1. Geometry of the tensor product of C*-algebras, Mathematical Proceedings of the Cambridge Philosophical Society 104 (1988), 119-127.
    2. Tracially completely bounded multilinear maps on C*-algebras, Journal of the London Mathematical Society 39 (1989), 514-524.
    3. A characterization of operator algebras (with Z-J. Ruan and A. M. Sinclair), Journal of Functional Analysis 89 (1990), 288-301.
    4. Invariant subspaces of an operator on L^2(T) composed of a multiplication and a translation (with A. M. Davie,) Journal of Operator Theory 23 (1990), 115-123.
    5. Tensor products which do not preserve operator algebras, Mathematical Proceedings of the Cambridge Philosophical Society 108 (1990), 395-403.
    6. Commutativity in operator algebras, Proceedings of the American Mathematical Society 109 (1990), 709-715.
    7. Tensor products of operator spaces (with V. I. Paulsen), Journal of Functional Analysis 99 (1991), 262-292.
    8. The standard dual of an operator space, Pacific Journal of Mathematics 153} (1992), 15-30.
    9. Explicit construction of universal operator algebras and applications to polynomial factorization (with V. I. Paulsen), Proceedings of the American Mathematical Society 112 (1991), 839-850.
    10. Some applications of a recent characterization of operator algebras, In “Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory”, Ed. R.S. Doran, Contemporary Mathematics, v. 120 AMS (1991).
    11. Tensor products of operator spaces II, Canadian Journal of Mathematics 44 (1992), 75-90.
    12. Generalizing Grothendieck's program, In "Function Spaces", Ed. K. Jarosz, Lecture Notes in Pure and Applied Math. Vol. 136, Marcel Dekker (1992).
    13. The dual of the Haagerup tensor product (with R. R. Smith), Journal of the London Mathematical Society 45 (1992), 126-144.
    14. A completely bounded characterization of operator algebras. Math. Annalen 303 (1995), 227-239.
    15. On quotients of function algebras, and operator algebra structures on l^p. (with C. Le Merdy), J. Operator Theory 34 (1995), 315-346.
    16. A generalization of Hilbert modules. J. Functional Analysis 136 (1996), 365-421.
    17. Factorizations in universal operator spaces and algebras. Rocky Mountain Journal of Mathematics 27 (1997), 151-167.
    18. Continuous functions on compact groups. Proceedings of the American Math. Society 125 (1997), 1177-1185.
    19. A new approach to C*-modules. Math. Annalen 307 (1997), 253-290.
    20. On selfdual Hilbert modules in Fields Institute Communications vol. 13, A.M.S (1997).
    21. Some general theory of operator algebras and their modules,} p.113-144 in "Operator Algebras and Applications", Ed. A. Katavolos, Nato ASI Series, Series C - Vol. 495, Kluwer (1997).
    22. Morita equivalence of operator algebras and their C*-envelopes, (with P.S. Muhly and Q. Na), Journal of the London Math. Soc. 31 (1999), 581-591.
    23. Modules over operator algebras and the maximal C*-dilation J. Functional Analysis 169 (1999), 251-288.
    24. Categories of operator modules - Morita equivalence and projective modules (with P.S. Muhly and V.I. Paulsen). 1998 revision. Memoirs of the American Math. Soc., Vol. 143 No. 681, January 2000.
    25. On Morita's fundamental theorem for C*-algebras, Math. Scand. 88 (2001), 137-153.
    26. A Morita theorem for Algebras of Operators on Hilbert Space, Journal of Pure and Applied Algebra 156 (2001), 153-169.
    27. On function and operator modules, (with C. Le Merdy) Proceedings of the American Math. Soc. 129 (2001), 833-844.
    28. The Shilov boundary of an operator space, and the characterization theorems, J. Functional Analysis 182 (2001), 280-343.
    29. Multipliers of operator spaces and the injective envelope, (with V. I. Paulsen) Pacific Journal of Mathematics, 200 ((2001), 1-14.
    30. Multipliers and dual operator algebras, J. Functional Analysis 183 (2001), 498-525.
    31. Isomorphisms of function modules and generalized approximation in modulus, (with K. Jarosz) Trans. Amer. Math. Soc. 354 (2002), 3663-3701.
    32. One-sided M-Ideals and Multipliers in Operator Spaces, I, (with E.G. Effros and V. Zarikian) Pacific Journal of Mathematics 206 (2002), 287-319.
    33. Complete isometries into C*-Algebras, (with D. Hay) Preprint (2002).
    34. Logmodularity and isometries of operator algebras, (with L. Labuschagne) Trans. Amer. Math. Soc. 355 (2002), 1621-1646.
    35. Complete isometries - an illustration of noncommutative functional analysis, (with D. Hay) Proceedings of 4th Conference on Function Spaces, Contemp. Math. Vol. 328, AMS (2003).
    36. Multipliers, C*-modules, and algebraic structure in spaces of Hilbert space operators Multipliers, $C^*$-modules, and algebraic structure in spaces of Hilbert space operators,} ``Operator Algebras, Quantization, and Noncommutative Geometry: A Centennial Celebration Honoring J. von Neumann and M. H. Stone" (2003). Click here
    37. The ideal envelope of an operator algebra, (with M. Kaneda) Proc. Amer. Math. Soc. 132 (2004), 2103-2113.
    38. One-sided ideals and approximate identities in operator algebras, J. Australian Math. Soc. 76 (2004), 425-447.
    39. One-Sided Projections on C*-Algebras, (with R. R. Smith and V. Zarikian) J. of Operator Theory 51 (2004), 201-220.
    40. A double commutant theorem for operator algebras, (with B. Solel) J. of Operator Theory 51 (2004), 435-453.
    41. Multiplier operator algebras and applications, (with V. Zarikian) Proceedings of the National Academy of Sciences of the U.S.A. 101 (2004), 727-731. This can be viewed from this link
    42. Are operator algebras Banach algebras? In Banach Algebras and Their Applications, Contemporary Mathematics 363, American Mathematical Society, 2004. This can be viewed from this link
    43. Duality and operator algebras: Automatic weak* continuity and applications (with B. Magajna), J. Functional Analysis 224 (2005), 386-407.
    44. Duality and operator algebras II: Operator algebras as Banach algebras (with B. Magajna), J. Functional Analysis 226 (2005), 485-493.
    45. The calculus of one-sided M-ideals and multipliers in operator spaces, (with V. Zarikian), Memoirs Amer. Math. Soc. 842 (2006).
    46. Ordered C*-modules (with Wend Werner), Proceedings of the London Mathematical Society 92 (2006), 682-712. .
    47. Characterizations of noncommutative H^\infty (with L. E. Labuschagne), Journal of Integral Equations and Operator Theory 56 (2006), 301-321 .
    48. Noncommutative function theory and unique extensions (with L. E. Labuschagne), Studia Math. 178 (2007), 177-195.
    49. Open partial isometries and positivity in operator spaces, (with M. Neal). Studia Math. 182(2007), 227-262.
    50. Ordered involutive operator spaces (with K. Kirkpatrick, M. Neal, W. Werner), Positivity 11 (2007), 497-510.
    51. Positivity in operator algebras and operator spaces. (Chapter in book). p. 27-71 in "Positivity", Trends in Mathematics series, Birkhauser (2007).
    52. Von Neumann algebraic H^p theory (with L. E. Labuschagne), in: Function spaces: 5th Conference on function spaces, Contemp. Math. Vol 435, Amer. Math. Soc (2007).
    53. A Beurling theorem for noncommutative L^p (with L. E. Labuschagne), Journal of Operator Theory 59 (2008), 29-51.
    54. Hereditary subalgebras of operator algebras (with D.M. Hay and M. Neal). Journal of Operator Theory 59 (2008), 333-357.
    55. Applications of the Fuglede-Kadison determinant: Szego's theorem and outers for noncommutative H^p (with L. E. Labuschagne). Transactions Amer. Math. Soc. 360 (2008), 6131--6147.
    56. Peak tripotents (Preprint).
    57. Extensions of operator algebras I and II (Part I, with M. Royce, appeared in J. Math. Analysis and Applns. 339 (2008), 1451--1467. Part II is available on request).
    58. Morita equivalence of dual operator algebras (with U. Kashyap) J. Pure and Applied Algebra 212 (2008), 2401-2412.
    59. On a generalization of $W^*$-modules, (with J. Kraus), Banach Center Publications 91 (2010), 77-86.
    60. A characterization and a generalization of W*-modules, (with U. Kashyap), Trans. Amer. Math. Soc. 363 (2011), 345-363.
    61. Nuclearity-related properties for nonselfadjoint algebras (with B. Duncan), J. Operator Theory 65 (2011), 47-70. Errata J. Operator Theory 65 (2011), 471-473.
    62. Metric characterizations of isometries and of unital operator spaces and systems (with M. Neal), Proc. Amer. Math. Soc. 139 (2011), 985-998.
    63. Dual operator systems (with B. Magajna), 2008, Bull. London Math. Soc. 43 (2011), 311--320.
    64. Operator algebras with contractive approximate identity, (with Charles Read), J. Functional Analysis 261 (2011), 188-217.
    65. Ideals and structure of operator algebras, (with M. Almus and S. Sharma), J. Operator Theory 67 (2012), 397--436.
    66. Open projections in operator algebras I: Comparison theory, (with Matthew Neal), Studia Math. 208 (2012), 117--150.
    67. Open projections in operator algebras II: Compact projections, (with Matthew Neal), Studia Math. 209 (2012), 203-224.
    68. Metric characterizations II, (with Matthew Neal), Illinois J. Math. 57 (2013), 25–41.
    69. Ideals and hereditary subalgebras of operator algebras, (with M. Almus and Charles Read), Studia Math. 212 (2012), 65--93.
    70. Operator algebras with contractive approximate identities II, (with Charles Read), J. Functional Analysis 264 (2013), 1049-1067.
    71. Noncommutative peak interpolation revisited, Bull. London Math. Soc. 45 (2013), 1100-1106.
    72. Outers for noncommutative $H^p$ revisited, (with L. E. Labuschagne), Studia Math 217 (2013), 265-287.
    73. Operator algebras with contractive approximate identities III, (with Charles Read), Preprint (2013). This paper has now been replaced by, and subsumed into, successors listed below.
    74. On positivity and roots in operator algebras, (with C. A Bearden and Sonia Sharma), J. Integral Equations Operator Th. 79 (2014), 555-566.
    75. Finite generation in C*-algebras and Hilbert C*-modules, (with Tomasz Kania), Studia Math. 224 (2014), 143–151.
    76. Operator algebras with contractive approximate identities: Weak compactness and the spectrum (with Charles Read), J. Functional Analysis 267 (2014), 1837--1850.
    77. Order theory and interpolation in operator algebras, (with Charles Read), Studia Math. 225 (2014), 61--95.
    78. Operator algebras with contractive approximate identities: a large operator algebra in c0 (with Charles Read), Trans. Amer. Math. Soc. 368 (2015), 3243--3270.
    79. Real positivity and approximate identities in Banach algebras, (with Narutaka Ozawa), Pacific Math. J. 277 (2015), 1–59. DOI 10.2140/pjm.2015.277.1
    80. Generalization of C*-algebra methods via real positivity for operator and Banach algebras, pages 35--66 in "Operator algebras and their applications: A tribute to Richard V. Kadison", (ed. by R. S. Doran and E. Park), vol. 671, Contemporary Mathematics, American Mathematical Society, Providence, R. I. 2016.
    81. Completely contractive projections on operator algebras, (with Matthew Neal), Pacific Journal of Mathematics 283-2 (2016), 289--324.
    82. Roots in Banach and operator algebras, (with Zhenhua Wang), J. Integral Equations Operator Theory 85 (2016), 63-90, DOI 10.1007/s00020-015-2272-z
    83. Quantum measurable cardinals (with N. Weaver), J. Functional Analysis 273 (2017), 1870--1890.
    84. Rigged modules I: modules over dual operator algebras and the Picard group} (with U. Kashyap), J. Pure and Applied Algebra 221 (2017), 2827–2837.
    85. Rigged modules II: Multipliers and duality, Studia Math. DOI: 10.4064/sm8671-9-2016, 236 (2017), 85-100.
    86. Ueda's peak set theorem for general von Neumann algebras (with L. Labuschagne), Trans. Amer. Math. Soc. 370 (2018), 8215--8236.
    87. Operator *-correspondences in analysis and geometry, (with Jens Kaad and Bram Mesland), Proc.\ London Math Soc. 117 (2018), 303-344.
    88. Jordan operator algebras, (with Zhenhua Wang), Mathematische Nachrichten, 291 (2018), 1629--1654.
    89. Noncommutative topology and Jordan operator algebras. (with Matt Neal), Mathematische Nachrichten, 292 (2019), 481--510.
    90. Lp operator algebras with approximate identities I (with N. Christopher Phillips), preprint 2018, Pacific Journal of Mathematics 303 (2019), 401--457.
    91. The Hoffman-Rossi theorem for operator algebras, (with Luis Flores and Beate Zimmer), 91 (2019) , J. Integral Equations Operator Theory 91 (2019) Art. 17, 7 pp, DOI: 10.1007/s00020-019-2521-7.
    92. Jordan operator algebras revisited, (with Zhenhua Wang), Mathematische Nachrichten 292 (2019), 2129--2136.
    93. Involutive operator algebras, (with Zhenhua Wang), Positivity 24 (2020), 13--53
    94. On vector-valued characters for noncommutative function algebras, (with L. Labuschagne), Complex Analysis and Operator Theory 14, 31 (2020). https://doi.org/10.1007/s11785-020-00989-1
    95. Contractive projections and real positive maps on operator algebras (with Matt Neal), Studia Math. 256 (2021), 21--60.
    96. Real positive maps and conditional expectations on operator algebras, p. 63--102 in {\em Positivity and its applications}, (Eds. E. Kikianty, M. Mabula, M. Messerschmidt, J. H. van der Walt, and M. Wortel), Trends in Mathematics, Birkhauser (2021).
    97. Real operator algebras and real positive maps (with W Tepsan), J. Integral Equations Operator Theory 90 (2021), no. 5, Paper No. 49.
    98. Von Neumann algebra conditional expectations with applications to generalized representing measures for noncommutative function algebras, (with L Labuschagne), 58 pages, Advances in Mathematics, 396 (2022), doi 10.1016/j.aim.2021.108104
    99. Abelian von Neumann algebras, measure algebras and $L^\infty$-spaces, (with S. Goldstein and Louis E. Labuschagne), Expositiones Mathematicae 40 (2022),758-818 (61 pages) DOI: 10.1016/j.exmath.2021.11.005
    100. A noncommutative Bishop peak interpolation-set theorem, Operators, Semigroups, Algebras and Function Theory, Operator Theory: Advances and Applications 292, Volume from IWOTA Lancaster 2021}, Birkhauser Cham (2023).
    101. Real operator spaces and operator algebras, 40 pages, Studia Math (also on ArXiV) DOI: 10.4064/sm230329-23-12, Published online 14 March 2024.
    102. Real structure in operator spaces, injective envelopes and $G$-spaces, (with A. Cecco and M. Kalantar), 27 pages, J. Integral Equations Operator Theory https://rdcu.be/dFGFC (also on ArXiV). doi 10.1007/s00020-024-02766-7
    103. Operator space complexification transfigured, (with M. Kalantar), International Mathematics Research Notices (2024) 26 pages, https://doi.org/10.1093/imrn/rnae026 (also on ArXiV).
    104. On a class of subdiagonal algebras, (with L Labuschagne), Complex analysis and operator theory (2024), 24 pages, doi 10.1007/s11785-024-01490-9. View pdf at https://rdcu.be/dAlgu
    105. M-ideals, yet again: the case of real JB*-triples, (with Matthew Neal; Antonio M. Peralta; Shanshan Su), 31 page preprint Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (Impact factor 1.8 2023). (2025) 119:23 https://doi.org/10.1007/s13398-024-01686-w ( View pdf at https://rdcu.be/d4mLj )
    106. Null projections and noncommutative function theory in operator algebras, (with Rapha\"el Clou\^atre), 39 page submitted preprint, ArXiV (2024).
    107. M-ideals in real operator algebras, (with Matthew Neal; Antonio M. Peralta; Shanshan Su), 17 page submitted preprint 2024, ArXiV.
    108. A missing theorem on dual spaces, 14 page preprint (2024) (ArXiV:2405.01133).
    109. Geometric influences on quantum Boolean cubes (with Li Gao and Bang Xu), submitted preprint 2024 (36 pages), arXiv:2409.00224.

Again, almost of the papers may be downloaded from the ArXiV site at https://arxiv.org Be warned however that the version that appears there is not the final revised version (even if it says that it is) - see the journal for that.

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