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Basic sequences and spaceability in l(p) spaces

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Cariello, Daniel and Seoane-Sepúlveda, Juan B. (2014) Basic sequences and spaceability in l(p) spaces. Journal of functional analysis, 266 (6). pp. 3797-3814. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123613004771




Abstract

Let X be a sequence space and denote by Z(X) the subset of X formed by sequences having only a finite number of zero coordinates. We study algebraic properties of Z(X) and show (among other results) that (for p is an element of [1, infinity]) Z(l(p)) does not contain infinite dimensional closed subspaces. This solves an open question originally posed by R.M. Aron and V.I. Gurariy in 2003 on the linear structure of Z(l(infinity)). In addition to this, we also give a thorough analysis of the existing algebraic structures within the sets Z(X) and X \ Z(X) and their algebraic genericities.


Item Type:Article
Uncontrolled Keywords:Lineability; Spaceability; Algebrability; Basic sequence; Complemented subspace; l(p) spaces
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:24990
Deposited On:07 Apr 2014 09:10
Last Modified:25 Nov 2016 12:30

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