Volume 36 • Number 4 • 2013   • Spectral Synthesis for the Operator Space Projective Tensor Product of $C*$-Algebras Ranjana Jain and Ajay Kumar Abstract. We study the spectral synthesis for the Banach $C$*-algebra, 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 $A\widehat{\bigotimes}B$ obeys spectral synthesis. The Banach algebra $A\widehat{\bigotimes}A$ with the reverse involution is also studied. 2010 Mathematics Subject Classification: 46L06, 46L07, 47L25, 43A45 Full text: PDF