Bilinear maps on C$^*$-algebras that have product property at a compact element

Jorge J. Garcés; Mykola Khrypchenko

Bilinear maps on C$^*$-algebras that have product property at a compact element

Operator Algebras 2023-12-04 v2 Functional Analysis

Authors: Jorge J. Garcés , Mykola Khrypchenko

Abstract

We study bounded bilinear maps on a C $^*$ -algebra $A$ having product property at $c\in A$ . This leads us to the question of when a C $^*$ -algebra is determined by products at $c.$ In the first part of our paper, we investigate this question for compact C $^*$ -algebras, and in the second part, we deal with von Neumann algebras having non-trivial atomic part. Our results are applicable to descriptions of homomorphism-like and derivation-like maps at a fixed point on such algebras.

Keywords

bounded bilinear maps c*-algebras product property compact c*-algebras von neumann algebras homomorphism-like maps derivation-like maps

Cite

@article{arxiv.2310.06595,
  title  = {Bilinear maps on C$^*$-algebras that have product property at a compact element},
  author = {Jorge J. Garcés and Mykola Khrypchenko},
  journal= {arXiv preprint arXiv:2310.06595},
  year   = {2023}
}

Comments

The manuscript has been revised according to the referee's suggestions and comments

Bilinear maps on C$^*$-algebras that have product property at a compact element

Abstract

Keywords

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