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LIPSCHITZ-TYPE INEQUALITIES FOR ANALYTIC FUNCTIONS IN BANACH ALGEBRAS
Published online by Cambridge University Press: 11 April 2019
Abstract
In this paper we provide some bounds for the quantity $\Vert f(y)-f(x)\Vert$, where $f:D\rightarrow \mathbb{C}$ is an analytic function on the domain $D\subset \mathbb{C}$ and $x$, $y\in {\mathcal{B}}$, a Banach algebra, with the spectra $\unicode[STIX]{x1D70E}(x)$, $\unicode[STIX]{x1D70E}(y)\subset D$. Applications for the exponential and logarithmic functions on the Banach algebra ${\mathcal{B}}$ are also given.
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MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 100 , Issue 3 , December 2019 , pp. 489 - 497
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.