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Moduleability, algebraic structures, and nonlinear properties

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García-Pacheco, F.J. and Pérez-Eslava, C. and Seoane-Sepúlveda, Juan B. (2010) Moduleability, algebraic structures, and nonlinear properties. Journal of Mathematical Analysis and Applications, 370 (1). pp. 159-167. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/journal/0022247X


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Abstract

We show that some pathological phenomena occur more often than one could expect, existing large algebraic structures (infinite dimensional vector spaces, algebras, positive cones or infinitely generated modules) enjoying certain special properties. In particular we construct infinite dimensional vector spaces of non-integrable, measurable functions, completing some recent results shown in Garcia-Pacheco et al. (2009) [13], Garcia-Pacheco and Seoane-Sepulveda (2006) [15], Munoz-Fernandez et al. (2008) [20]. We prove, as well, the existence of dense and not barrelled spaces of sequences every non-zero element of which has a finite number of zero coordinates (giving partial answers to a problem originally posed by R.M. Aron and V.I. Gurariy in 2003).


Item Type:Article
Uncontrolled Keywords:Lineability; Spaceability; Algebrability; Differentiable functions; Measurable functions; Integrable functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:19988
Deposited On:18 Feb 2013 14:13
Last Modified:28 Nov 2016 08:15

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