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Cariello, Daniel and SeoaneSepúlveda, Juan B. (2014) Basic sequences and spaceability in l(p) spaces. Journal of functional analysis, 266 (6). pp. 37973814. ISSN 00221236

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

http://www.sciencedirect.com/  Publisher 
http://arxiv.org/pdf/1307.2508v1.pdf  Organisation 
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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