Spectral synthesis for operator space projective tensor product of $C^{\ast }$-algebras

Abstract

We study the spectral synthesis for the Banach *-algebra $A\oop B$, the operator space projective tensor product of $C^{\ast }$-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.

References in corpus (1)

• Ideals in Operator Space Projective Tensor Product of $C^{\ast }$-algebras

Cited by in corpus (2)

• Projective Tensor Products of $C^{\ast }$-algebras
• ${}^{\ast }$-Regularity of Operator Space Projective Tensor Product of C${}^{\ast }$-Algebras