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

2023/10/10 by Jorge J. Garcés, Mykola Khrypchenko, Garcés, Jorge J. +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.2310.06595

Abstract

We study bounded bilinear maps on a C^*-algebra A having product property at c∈ 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.

Related

• Bilinear maps having Jordan product property
• Factorization of completely bounded bilinear operators and injectivity
• Projective Tensor Products of C^*-algebras
• Characterizing linear mappings through zero products or zero Jordan products
• Zero product preservers of C*-algebras