# Ideal in projective tensor product of Banach algebras [closed]

Let $A,B$ be Banach algebras and $A\hat{\otimes}B$ be projective tensor product of them. Let $S$ be an ideal of $A\hat{\otimes}B$. Are there ideals $I$ of $A$ and $J$ of $B$ such that $S=I\hat{\otimes}J$?

Thanks

## closed as off-topic by Yemon Choi, Stefan Kohl, András Bátkai, Chris Godsil, Marco GollaSep 18 '15 at 7:01

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – Stefan Kohl, András Bátkai, Chris Godsil, Marco Golla
If this question can be reworded to fit the rules in the help center, please edit the question.

• I'm voting to close this question as off-topic because it should have been though through more carefully, by considering finite-dimensional cases – Yemon Choi Sep 17 '15 at 16:31