Strong Morita equivalence of operator spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Eleftherakis, George K.¹  Kakariadis, Evgenios T. A.² 

[1] Univ Patras, Fac Sci, Dept Math, Patras 26504, Greece

[2] Newcastle Univ, Sch Math & Stat, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

关键词: Operator spaces;    Ternary ring of operators;    Morita contexts for operator algebras;    TRO envelope;    C*-envelope;   

DOI  :  10.1016/j.jmaa.2016.09.042

来源: Elsevier

【 摘 要 】

We introduce and examine the notions of strong Delta-equivalence and strong TRO equivalence for operator spaces. We show that they behave in an analogous way to how strong Morita equivalence does for the category of C*-algebras. In particular, we prove that strong Delta-equivalence coincides with stable isomorphism under the expected countability hypothesis, and that strongly TRO equivalent operator spaces admit a correspondence between particular representations. Furthermore we show that strongly Delta-equivalent operator spaces have stably isomorphic second duals and strongly Delta-equivalent TRO envelopes. In the case of unital operator spaces, strong Delta-equivalence implies stable isomorphism of the C*-envelopes. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free