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Tbilisi Mathematical Journal

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Vector norm inequalities for power series of operators in Hilbert spaces

W.-S. Cheung
  • Corresponding author
  • Department of Mathematics, University of Hong Kong, Pokfulam Road, Hong Kong, China
  • Other articles by this author:
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/ S.S. Dragomir
  • Corresponding author
  • Mathematics, School of Engineering & Science, Victoria University, PO Box 14428, Melbourne City, MC 8001, Australia
  • School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
  • Other articles by this author:
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Published Online: 2014-12-30 | DOI: https://doi.org/10.2478/tmj-2014-0013


In this paper, vector norm inequalities that provides upper bounds for the Lipschitz quantity ║f (T) x - f (V ) x ║ for power series f(z) = ∑n=0 anzn; bounded linear operators T; V on the Hilbert space H and vectors x ∈ H are established. Applications in relation to Hermite- Hadamard type inequalities and examples for elementary functions of interest are given as well.

Keywords: Bounded linear operators; Hilbert spaces; Functions of operators; Power series; Hermite-Hadamard type inequal- ities


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Published Online: 2014-12-30

Citation Information: Tbilisi Mathematical Journal, Volume 7, Issue 2, ISSN (Online) 1512-0139, DOI: https://doi.org/10.2478/tmj-2014-0013.

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