Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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).

Do there exist two infinite-dimensional Banach algebras $A, B$ such that $\mathcal{B}(H)$ is isomorphic as a Banach algebra to the projective tensor product $A\otimes_\gamma B$?

share|cite|improve this question
Now cross-posted to MathOverflow: – user16299 Sep 26 '12 at 22:09
I just now that the projective tensor product oh $H$ and $H^*$ is B(H). – Ali Bagheri Jan 23 at 14:01

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.