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Remarks on Commuting Functions of Operators

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Let A, B be bounded linear operators on a Hilbert space and f, g two functions defined on the spectra \(\sigma (A)\) and \(\sigma (B)\), respectively. In this paper, we study the following general problem: when does \(f(A)g(B)=g(B)f(A)\) imply \(AB=BA\)? We also study this problem for normal operators and we give sufficient conditions for the normality of the n-th root and the logarithm of a normal operator.

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  1. St Francis College, New York, NY, USA

    Fotios C. Paliogiannis

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  1. Fotios C. Paliogiannis
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Correspondence to Fotios C. Paliogiannis.

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Paliogiannis, F.C. Remarks on Commuting Functions of Operators. Complex Anal. Oper. Theory 17, 83 (2023). https://doi.org/10.1007/s11785-023-01388-y

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