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December 2021 Norm inequalities for the generalised commutator in Banach algebras
Silvestru Sever Dragomir
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SUT J. Math. 57(2): 185-199 (December 2021). DOI: 10.55937/sut/1641859472

Abstract

In this paper, by utilising the Riesz functional calculus in a Banach algebra $\mathcal{B}$, we provide some norm inequalities for the generalized commutator $$f(y)z-zf(x)$$ where $x,$ $y,$ $z\in \mathcal{B}$ and $f$ is an analytic function for which the elements $f(y)$ and $f(x)$ exist. Some examples for the resolvent and exponential functions are also given.

Acknowledgments

The author would like to thank the anonymous referee for valuable suggestions that have been implemented in the final version of the manuscript.

Citation

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Silvestru Sever Dragomir. "Norm inequalities for the generalised commutator in Banach algebras." SUT J. Math. 57 (2) 185 - 199, December 2021. https://doi.org/10.55937/sut/1641859472

Information

Received: 11 May 2021; Published: December 2021
First available in Project Euclid: 21 April 2022

Digital Object Identifier: 10.55937/sut/1641859472

Subjects:
Primary: 47A63 , 47A99

Keywords: analytic functions , axponential and logarithmic function on Banach algebra , Banach algebras , Lipschitz type inequalities

Rights: Copyright © 2021 Tokyo University of Science

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Vol.57 • No. 2 • December 2021
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