Note on Wermuth's theorem on commuting operator exponentials

2019/01/29 by Krzysztof Szczygielski, Szczygielski, Krzysztof
Computer Science · Mathematics · #16S99 #47L10 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1901.10261

openalex publication_date 2019/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply Wermuth's theorem on commuting operator exponentials to show that if A, B ∈ B(X), X being Banach space and A of 2πi-congruence free spectrum, then e^A B = B e^A if and only if AB=BA. We employ this observation to provide alternative proof of similar result by Chaban and Mortad, applicable for X being a Hilbert space.

Related

• Non-commutativity of exponential spectrum
• Commutators close to the identity
• Counterexamples Related to Commutators of Unbounded Operators
• Perturbations not necessarily commutative
• Commutators greater than a perturbation of the identity