Note on Wermuth's theorem on commuting operator exponentials

Krzysztof Szczygielski

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arXiv · 1901.10261

Note on Wermuth's theorem on commuting operator exponentials

Krzysztof Szczygielski

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Abstract

We apply Wermuth's theorem on commuting operator exponentials to show that if $A, B \in B(X)$, $X$ being Banach space and $A$ of $2\pi i$-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.

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Krzysztof Szczygielski. 2019-01-29. Note on Wermuth's theorem on commuting operator exponentials. https://arxiv.org/abs/1901.10261

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