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Journal of Mathematical Analysis and Applications
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Journal of Mathematical Analysis and Applications
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Normal Structure in James Spaces

Normal structure in James spaces
Authors: Khamsi, M.A.; Swaminathan, S.;

Normal Structure in James Spaces

Abstract

Let \(X\) be a Banach space with a basis \((x_n)\). Let \(c_0\) be the space of all real sequences that converges to \(0\). The famous James space \(J(X)\) [\textit{R. C. James}, Proc. Natl. Acad. Sci. USA 37, 174-177 (1951; Zbl 0042.36102)] consists of all sequences \((\alpha_n)\in c_0\) for which \[ \sup\Biggl\{\Biggl|\sum_{1\leq i\leq n}(\alpha_{p_i}- \alpha_{p_{i+1}}) x_i+(\alpha_{p_{n+1}}- \alpha_{p_1}) x_{n+1}\Biggr|\Biggr\}<\infty, \] the supremum being taken over all finite increasing sequences of positive numbers \(p_1,p_2,\dots, p_{n+1} \). In this interesting paper, the authors have proved the following important result about the normal structure property of James space \(J(X)\). Main Theorem: Let \(X\) be a Banach space with a basis which is symmetric, boundedly complete, 1-unconditional, and uniformly monotone. Then \(J(X)\) has the normal structure property.

Keywords

symmetric, Banach space with a basis, Applied Mathematics, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, normal structure, 1-unconditional, James space, Geometry and structure of normed linear spaces, boundedly complete, uniformly monotone, Classical Banach spaces in the general theory, Analysis

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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