Mahmood POURGHOLAMHOSSEIN
,
Mohammad ROUZBEHANI
,
Massoud AMINI
. CHAIN CONDITIONS FOR C*-ALGEBRAS COMING FROM HILBERT C*-MODULES[J]. Acta mathematica scientia, Series B, 2018
, 38(4)
: 1163
-1173
.
DOI: 10.1016/S0252-9602(18)30806-3
[1] Akemann C A, Amini M, Asadi M B. Which multiplier algebras are W*-algebras? J Operator Theory, 2013, 74:125-132
[2] Bakic D, Guljas B. On a class of module maps of Hilbert C*-modules. Math Commun, 2002, 7(2):177-192
[3] Beer W. On Morita equivalence of nuclear C*-algebras. J Pure Appl Algebra, 1982, 26:249-267
[4] Blackadar B. Operator Algebras, Theory of C*-algebras and von Neumann Algebras. Berlin:Springer, 2006
[5] Bratteli O, Elliott G A. Structure spaces of approximately finite-dimensional C*-algebras, Ⅱ. J Funct Anal, 1978, 30:74-82
[6] Goubault-Larrecq J. On Noetherian spaces//Proc 22nd IEEE Int Symp Logic in Computer Science (LICS 2007), Wroclaw, Poland, 2007:453-462
[7] Hines T, Walsberg E. Nontrivially Noetherian C*-algebras. Math Scand, 2012, 111:135-146
[8] Huef A A, Williams D N, Raeburn I. Properties preserved under Morita equivalence of C*-algebras. Proc Amer Math Soc, 2007, 135(5):1495-1503
[9] Joita M, Moslehian M S. A Morita equivalence for Hilbert C*-modules. Stud Math, 2012, 209:11-19
[10] Kaplanski I. Modules over operator algebras. Amer J Math, 1953, 75(4):839-853
[11] Kasparov G G. Hilbert C*-modules:Theorems of Stinespring and Voiculescu. J Oper Theory, 1980, 4:133-150
[12] Khoshkam M. Hilbert C*-modules and conditional expectations on crossed products. J Austral Math Soc, 1996, 61:106-118
[13] Kirchberg E, Rordam M. Non-simple purely infinite C*-algebras. Amer J Math, 2000, 122:637-666
[14] Lance H C. Hilbert C*-Modules, A Toolkit for Operator Algebraists. London Mathematical Society Lecture Note Series 210. Cambridge:Cambridge University Press, 1995
[15] Lin H. Injective Hilbert C*-modules. Pacific J Math, 1992, 154:131-164
[16] Manuilov V M, Troitsky E V. Hilbert C*-Modules. Trans Math Monographs 226. Providence:Amer Math Soc, 2005
[17] Murphy G J. C*-Algebras and Operator Theory. San Diego:Academic Press, 1990
[18] Pasnicu C, Rordam M. Tensor products of C*-algebras with the ideal property. J Funct Anal, 2000, 17:130-137
[19] Pasnicu C, Rordam M. Purely infinite C*-algebras of real rank zero. J Reine Angew Math, 2007, 613:51-73
[20] Paschke W L. Inner product modules over B*-algebras. Trans Amer Math Soc, 1973, 182:443-468
[21] Raeburn I, Williams D P. Morita Equivalence and Continuous-Trace C*-Algebras. Mathematical Surveys and Monographs 60. Providence:Amer Math Soc, 1998
[22] Rieffel M A. Induced representations of C*-algebras. Adv Math, 1974, 13(2):176-257
[23] Rieffel M A. Actions of finit groups on C*-algebras. Math Scand, 1980, 47:157-176
[24] Rieffel M A. Morita equivalence for operator algebras. Proceedings of Symposia in Pure Mathematics, American Mathematical Society, 1982, 38:176-257
[25] Rordam M, Sierakowski A. Purely infinite C*-algebras arising from crossed products. Ergod Theory & Dynam Sys, 2012, 32:273-293
[26] Sinclair A M, Tullo A W. Noetherian Banach algebras are finite dimensional. Math Ann, 1974, 211:151-153
[27] Troitsky E V. Conditional expectations of finite index and properties of modules arising from group actions. J Math Sci, 2004, 123:4340-4362
[28] Watatani Y. Index for C*-subalgebras. Mem Amer Math Soc, 1990, 83(424):1-117