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
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
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