On stable maps of operator algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Eleftherakis, G. K.¹ 

[1] Univ Patras, Dept Math, Fac Sci, Patras 26500, Greece

关键词: Operator algebras;    C*-algebras;    TRO;    Stable isomorphism;    Morita equivalence;   

DOI  :  10.1016/j.jmaa.2018.12.031

来源: Elsevier

【 摘 要 】

We define a strong Morita-type equivalence similar to(sigma Delta) for operator algebras. We prove that A similar to(sigma Delta) B if and only if A and B are stably isomorphic. We also define a relation subset of(sigma Delta) for operator algebras. We prove that if A and B are C*-algebras, then A subset of(sigma Delta) B if and only if there exists an onto *-homomorphism theta : B circle times K -> A circle times K, where K is the set of compact operators acting on an infinite dimensional separable Hilbert space. Furthermore, we prove that if A and B are C*-algebras such that A subset of(sigma Delta) B and B subset of(sigma Delta) A, then there exist projections r, (r) over cap in the centers of A** and B**, respectively, such that Ar similar to(sigma Delta) B (r) over cap and A(id(A**) - r) similar to(sigma Delta) B(id(B**) - (r) over cap). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free