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Linear structure of sets of divergent sequences and series

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Aizpuru, A. and Pérez Eslava, C. and Seoane-Sepúlveda, Juan B. (2006) Linear structure of sets of divergent sequences and series. Linear Algebra and its Applications, 418 (2-3). pp. 595-598. ISSN 0024-3795

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Official URL: http://www.sciencedirect.com/science/article/pii/S0024379506001315


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Abstract

We show that there exist infinite dimensional spaces of series, every non-zero element of which, enjoys certain pathological property. Some of these properties consist on being (i) conditional convergent, (ii) divergent, or (iii) being a subspace of l(infinity) of divergent series. We also show that the space 1(1)(omega)(X) of all weakly unconditionally Cauchy series in X has an infinite dimensional vector space of non-weakly convergent series, and that the set of unconditionally convergent series on X contains a vector space E, of infinite dimension, so that if x is an element of E \ {0} then Sigma(i) parallel to x(i)parallel to = infinity.


Item Type:Article
Uncontrolled Keywords:Lineability; Conditionally convergent series; Divergent series; Vector series
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20212
Deposited On:04 Mar 2013 15:21
Last Modified:25 Nov 2016 12:48

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