Strong Morita equivalence of operator spaces

详细信息    查看全文

• 作者：George K. Eleftherakis^a ; ^{gelefth@math.upatras.gr" class="auth_mail" title="E-mail the corresponding author} ; Evgenios T.A. Kakariadis^b ; ^{evgenios.kakariadis@ncl.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Operator spaces ; Ternary ring of operators ; Morita contexts for operator algebras ; TRO envelope ; C*-envelope
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：446
• 期：2
• 页码：1632-1653
• 全文大小：501 K

文摘

We introduce and examine the notions of strong Δ-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 Δ-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 Δ-equivalent operator spaces have stably isomorphic second duals and strongly Δ-equivalent TRO envelopes. In the case of unital operator spaces, strong Δ-equivalence implies stable isomorphism of the C*-envelopes.