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Mathematica Slovaca

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Volume 60, Issue 3

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Some topological and geometric properties of generalized Euler sequence space

Emrah Kara / Mahpeyker Öztürk / Metin Bašarir
Published Online: 2010-05-13 | DOI: https://doi.org/10.2478/s12175-010-0019-5

Abstract

In this paper, we introduce the Euler sequence space e r(p) of nonabsolute type and prove that the spaces e r(p) and l(p) are linearly isomorphic. Besides this, we compute the α-, β- and γ-duals of the space e r(p). The results proved herein are analogous to those in [ALTAY, B.—BASŠAR, F.: On the paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 26 (2002), 701–715] for the Riesz sequence space r q(p). Finally, we define a modular on the Euler sequence space e r(p) and consider it equipped with the Luxemburg norm. We give some relationships between the modular and Luxemburg norm on this space and show that the space e r(p) has property (H) but it is not rotund (R).

MSC: Primary 46A45, 46B45; Secondary 46E30, 46B20

Keywords: Euler sequence space; paranormed sequence space; α-; β-; γ-duals; property (H); rotund property; LUR property

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About the article

Published Online: 2010-05-13

Published in Print: 2010-06-01


Citation Information: Mathematica Slovaca, Volume 60, Issue 3, Pages 385–398, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-010-0019-5.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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