most recent 30 from http://mathoverflow.net 2013-05-19T08:14:30Z http://mathoverflow.net/feeds/question/108188 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108188/tensorial-decomposition-of-bh TrzyTrypy 2012-09-26T18:30:23Z 2012-09-27T10:14:41Z

<p>Let $H$ be an infinite-dimensional Hilbert space and let $\mathcal{B}(H)$ be the (C*/W*-)algebra of bounded operators on it. Actually, you may forget about the involution in $\mathcal{B}(H)$ because I am interested in $\mathcal{B}(H)$ only as a Banach algebra (operator algebra).</p> <p>Do there exist two <strong>infinite-dimensional</strong> Banach algebras $A, B$ such that $\mathcal{B}(H)$ is isomorphic as a Banach algebra to the <strong>projective tensor product</strong> $A\otimes_\gamma B$?</p> <p>You may also replace the projective tensor product by any other Banach algebra tensor product which arises from a <strong>reasonable crossnorm</strong> (so the vNA tensor product is not good).</p>