Spectral synthesis for operator space projective tensor product of $C^*$-algebras

Details Spectral synthesis for operator space projective tensor product of $C^*$-algebras Spectral synthesis for operator space projective tensor product of $C^*$-algebras

2011-08-16

arxiv.org/abs/1108.3208v2

Mathematics

Operator Algebras

Scientific paper

We study the spectral synthesis for the Banach *-algebra $A\oop B$, the
operator space projective tensor product of $C^*$-algebras $A$ and $B$. It is
shown that if $A$ or $B$ has finitely many closed ideals, then $A\oop B$ obeys
spectral synthesis. The Banach algebra $A \oop A$ with the reverse involution
is also studied.

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