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Lineability in subsets of measure and function spaces


Muñoz-Fernández, Gustavo A. and Palmberg, M. and Puglisi, D. and Seoane Sepúlveda, Juan Benigno (2008) Lineability in subsets of measure and function spaces. Linear Algebra and its Applications, 428 (11-12). pp. 2805-2812. ISSN 0024-3795

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We show, among other results, that if lambda denotes the Lebesgue measure on the Borel sets in [0, 1] and X is an infinite dimensional Banach space, then the set of measures whose range is neither closed nor convex is lineable in ca(lambda, X). We also show that, in certain situations, we have lineability of the set of X-valued and non-sigma-finite measures with relatively compact range. The lineability of sets of the type L-p(I)\L-q (I) is studied and some open questions are proposed. Some classical techniques together with the converse of the Lyapunov Convexity Theorem are used.

Item Type:Article
Uncontrolled Keywords:Lineability; Spaceability; Linear spaces; Measure space; Injective measure; Function spaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:17086

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