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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 64, Issue 6

Issues

Generalized Orlicz-Lorentz sequence spaces and corresponding operator ideals

Manjul Gupta / Antara Bhar
Published Online: 2015-01-10 | DOI: https://doi.org/10.2478/s12175-014-0287-6

Abstract

In this paper we introduce generalized or vector-valued Orlicz-Lorentz sequence spaces l p,q,M(X) on Banach space X with the help of an Orlicz function M and for different positive indices p and q. We study their structural properties and investigate cross and topological duals of these spaces. Moreover these spaces are generalizations of vector-valued Orlicz sequence spaces l M(X) for p = q and also Lorentz sequence spaces for M(x) = x q for q ≥ 1. Lastly we prove that the operator ideals defined with the help of scalar valued sequence spaces l p,q,M and additive s-numbers are quasi-Banach operator ideals for p < q and Banach operator ideals for p ≥ q. The results of this paper are more general than the work of earlier mathematicians, say A. Pietsch, M. Kato, L. R. Acharya, etc.

MSC: Primary 46A45, 47B06, 47L20

Keywords: Lorentz sequence spaces; s-numbers of operators; Orlicz function and Orlicz sequence spaces; operator ideals

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About the article

Published Online: 2015-01-10

Published in Print: 2014-12-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 6, Pages 1475–1496, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-014-0287-6.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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