Automorphisms of Banach space projective tensor product of C*-algebras

2018/10/05 by Jain, Ranjana
#46L06 #46L40 #46M05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1810.02774

Abstract

For unital C^*-algebras A and B, we completely characterize the isometric (*-) automorphisms of their Banach space projective tensor product A⊗^γB. This leads to the characterization of inner and outer isometric *-automorphisms of A⊗^γB, 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 A⊗^γB coincides with U(A) ⊗ U(B), where U(A) is the unitary group of A. We also establish the fact that the relative commutant of A⊗^γℂ 1 in A ⊗^γB is same as Z(A) ⊗^γB, where B is a subhomogenous unital C^*-algebra, and A is any C^*-algebra.

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