Isomorphism of categories of rigged modules via completely bounded isomorphism of operator algebras - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T03:35:11Z http://mathoverflow.net/feeds/question/35280 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/35280/isomorphism-of-categories-of-rigged-modules-via-completely-bounded-isomorphism-of Isomorphism of categories of rigged modules via completely bounded isomorphism of operator algebras Kolya Ivankov 2010-08-11T21:42:43Z 2010-08-12T12:31:30Z <p>This question is a background for my previous question. </p> <p>Suppose $A$ and $B$ are two algebras over $\mathbb{C}$ with the sequences of norms $\lbrace\|\cdot\|_{\Xi,n}\rbrace$ and on $M_n(\Xi)$, $\Xi\in\lbrace A, B\rbrace$, satisfying the conditions of Blecher-Ruan-Sinclar <a href="http://www.jstor.org/pss/2160382" rel="nofollow">theorem</a> (so that, if I understand it right, we may construct concrete representations). Suppose also that $f\colon A \to B$ is a completely bounded map that has a completely bounded inverse $f^{-1}\colon B\to A$.</p> <p> Can we somehow establish an isomorphism between categories of rigged modules over $A$ and $B$. And if yes, is there any good reference? </p> <p>It can probably fit into the notion of <a href="http://www.ams.org/bookstore-getitem/item=MEMO-143-681" rel="nofollow">(P)-context</a>, but I can't reach the book right now to check all the conditions.</p>