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2014 Vector norm inequalities for power series of operators in Hilbert spaces
W.-S. Cheung, S.S. Dragomir
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Tbilisi Math. J. 7(2): 21-34 (2014). DOI: 10.2478/tmj-2014-0013

Abstract

In this paper, vector norm inequalities that provides upper bounds for the Lipschitz quantity $\left\Vert f\left( T\right) x-f\left( V\right)x\right\Vert $ for power series $f\left( z\right) =\sum_{n=0}^{\infty}a_{n}z^{n},$ bounded linear operators $T,V$ on the Hilbert space $H$ and vectors $x\in H$ are established. Applications in relation to Hermite-Hadamard type inequalities and examples for elementary functions of interest are given as well.

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W.-S. Cheung. S.S. Dragomir. "Vector norm inequalities for power series of operators in Hilbert spaces." Tbilisi Math. J. 7 (2) 21 - 34, 2014. https://doi.org/10.2478/tmj-2014-0013

Information

Received: 22 October 2014; Accepted: 3 December 2014; Published: 2014
First available in Project Euclid: 12 June 2018

zbMATH: 1320.47013
MathSciNet: MR3313052
Digital Object Identifier: 10.2478/tmj-2014-0013

Subjects:
Primary: 47A63
Secondary: 47A99

Rights: Copyright © 2014 Tbilisi Centre for Mathematical Sciences

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Vol.7 • No. 2 • 2014
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