Morita Equivalence for C*-Algebras with the Dunford-Pettis Property and C-Crossed Products

AbstractLet A and B be arbitrary C*-algebras, we prove that the existence of a Hilbert A–B-bimodule of finite index ensures that the WEP, QWEP, and LLP along with other finite-dimensional approximation properties such as CBAP and (S)OAP are shared by A and B. For this, we first study the stability of the WEP, QWEP, and LLP under Morita equivalence of C*-algebras. We present examples of Hilbert A–B-bimodules, which are not of finite index, while such properties are shared between A and B. To this end, we study twisted crossed products by amenable discrete groups.

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Strong Morita Equivalence for Heisenberg C*-Algebras and the Positive Cones of Their K 0-Groups

Canadian Journal of Mathematics ◽

10.4153/cjm-1988-037-8 ◽

1988 ◽

Vol 40 (04) ◽

pp. 833-864 ◽

Cited By ~ 2

Author(s):

Judith A. Packer

Keyword(s):

Heisenberg Group ◽

Morita Equivalence ◽

Equivalence Classes ◽

Crossed Products ◽

C Algebras ◽

Projective Representations ◽

Discrete Heisenberg Group ◽

Strong Morita Equivalence

In [14] we began a study of C*-algebras corresponding to projective representations of the discrete Heisenberg group, and classified these C*-algebras up to *-isomorphism. In this sequel to [14] we continue the study of these so-called Heisenberg C*-algebras, first concentrating our study on the strong Morita equivalence classes of these C*-algebras. We recall from [14] that a Heisenberg C*-algebra is said to be of class i, i ∊ {1, 2, 3}, if the range of any normalized trace on its K 0 group has rank i as a subgroup of R; results of Curto, Muhly, and Williams [7] on strong Morita equivalence for crossed products along with the methods of [21] and [14] enable us to construct certain strong Morita equivalence bimodules for Heisenberg C*-algebras.

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Crossed Products of pro-C*-Algebras and Morita Equivalence

Mediterranean Journal of Mathematics ◽

10.1007/s00009-008-0162-1 ◽

2008 ◽

Vol 5 (4) ◽

pp. 467-492 ◽

Cited By ~ 3

Author(s):

Maria Joiţa

Keyword(s):

Morita Equivalence ◽

Crossed Products ◽

C Algebras

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Strong Morita equivalence for inclusions of $C^*$-algebras induced by twisted actions of a countable discrete group

MATHEMATICA SCANDINAVICA ◽

10.7146/math.scand.a-125997 ◽

2021 ◽

Vol 127 (2) ◽

pp. 317-336

Author(s):

Kazunori Kodaka

Keyword(s):

Discrete Group ◽

Morita Equivalence ◽

Crossed Product ◽

Crossed Products ◽

C Algebra ◽

C Algebras ◽

Morita Equivalent ◽

Countable Discrete Group ◽

Relative Commutant ◽

Strong Morita Equivalence

We consider two twisted actions of a countable discrete group on $\sigma$-unital $C^*$-algebras. Then by taking the reduced crossed products, we get two inclusions of $C^*$-algebras. We suppose that they are strongly Morita equivalent as inclusions of $C^*$-algebras. Also, we suppose that one of the inclusions of $C^*$-algebras is irreducible, that is, the relative commutant of one of the $\sigma$-unital $C^*$-algebra in the multiplier $C^*$-algebra of the reduced twisted crossed product is trivial. We show that the two actions are then strongly Morita equivalent up to some automorphism of the group.

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