Morita embeddings for dual operator algebras and dual operator spaces
Volume 243 / 2018
Studia Mathematica 243 (2018), 303-328
MSC: Primary 47L05; Secondary 47L25, 47L35, 47L45, 46L10, 16D90.
DOI: 10.4064/sm170427-15-8
Published online: 19 March 2018
Abstract
We define a relation $\subset _\varDelta $ for dual operator algebras: $B\subset _\varDelta A$ if there exists a projection $p\in A$ such that $B$ and $pAp$ are Morita equivalent in the sense of Eleftherakis (2008). We show that $\subset _\varDelta $ is transitive, and we investigate the following question: If $A\subset _\varDelta B$ and $B\subset _\varDelta A$, are $A$ and $B$ stably isomorphic? We propose an analogous relation $\subset _\varDelta $ for dual operator spaces, and we present some properties of $\subset _\varDelta $ in this case.
