Strong Morita equivalence of operator spaces

Autor: Eleftherakis, George K., Kakariadis, Evgenios T. A.
Rok vydání: 2016
Předmět:
Zdroj: Journal of Mathematical Analysis and Applications 446 (2017), no.2, 1632-1653
Druh dokumentu: Working Paper
Popis: 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.
Comment: 25 pages; changes to the text; some proofs were shortened; for the expanded proofs see the previous version
Databáze: arXiv
načítá se...