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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

PDF
Restringido a Repository staff only 92kB |

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

## 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 |
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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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