Maps on self-adjoint operators preserving some relations related to commutativity

2024/02/14 by Mahdi Karder, Karder, Mahdi, Tatjana Petek +1
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2402.09227

openalex publication_date 2024/02/14 · openalex created_date 2024/02/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we give the complete description of maps on self-adjoint bounded operators on Hilbert space which preserve a triadic relation involving the difference of operators and either commutativity or quasi-commutativity in both directions. We show that those maps are implemented by unitary or antiunitary equivalence and possible additive perturbation by a scalar operator.

Related

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• Commutativity preserving transformations on conjugacy classes of finite\n rank self-adjoint operators
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• Counterexamples Related to Commutators of Unbounded Operators
• Essential Self-Adjointness of Anti-Commutative Operators