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- W2895573283 abstract "For unital $C^*$-algebras $A$ and $B$, we completely characterize the isometric ($*$-) automorphisms of their Banach space projective tensor product $Aotimes^gamma B$. This leads to the characterization of inner and outer isometric $*$-automorphisms of $Aotimes^gamma B$, as well. As an application, we provide a partial affirmative answer to a question posed by Kaijser and Sinclair, viz., we prove that for unital $C^*$-algebras $A$ and $B$, the set of norm-one unitaries of $Aotimes^gamma B$ coincides with $U(A) otimes U(B)$, where $U(A)$ is the unitary group of $A$. We also establish the fact that the relative commutant of $Aotimes^gamma mathbb{C} 1$ in $A otimes^gamma B$ is same as $Z(A) otimes^gamma B$, where $B$ is a subhomogenous unital $C^*$-algebra, and $A$ is any $C^*$-algebra." @default.
- W2895573283 created "2018-10-12" @default.
- W2895573283 creator A5079672245 @default.
- W2895573283 date "2018-10-05" @default.
- W2895573283 modified "2023-09-27" @default.
- W2895573283 title "Automorphisms of Banach space projective tensor product of C*-algebras" @default.
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