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

TL;DR
This paper characterizes isometric automorphisms of the Banach space projective tensor product of unital C*-algebras, providing insights into their structure and answering a question about unitaries in this tensor product.
Contribution
It offers a complete characterization of automorphisms of the tensor product of C*-algebras and addresses a specific open question about unitaries.
Findings
Characterization of isometric automorphisms of A⊗^γ B
Identification of unitaries in the tensor product as U(A)⊗U(B)
Description of the relative commutant in the tensor product
Abstract
For unital -algebras and , we completely characterize the isometric (-) automorphisms of their Banach space projective tensor product . This leads to the characterization of inner and outer isometric -automorphisms of , 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 -algebras and , the set of norm-one unitaries of coincides with , where is the unitary group of . We also establish the fact that the relative commutant of in is same as , where is a subhomogenous unital -algebra, and is any -algebra.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
