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Distinguished subspaces of L-p of maximal dimension

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Botelho, Geraldo and Cariello, Daniel and Favaro, Vinicius V. and Pellegrino, Daniel and Seoane-Sepúlveda, Juan B. (2013) Distinguished subspaces of L-p of maximal dimension. Studia Mathematica, 215 (3). pp. 261-280. ISSN 0039-3223

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Abstract

Let (Omega, Sigma, mu) be a measure space and 1 < p < infinity. We show that, under quite general conditions, the set L-p(Omega) - boolean OR(1 <= q<p) L-q(Omega) is maximal spaceable, that is, it contains (except for the null vector) a closed subspace F of L-p(Omega) such that dim (F) = dim (L-p (Omega)) This result is so general that we had to develop a hybridization technique for measure spaces in order to construct a space such that the set L-p(Omega) - L-q (Omega),1 <= q < p, fails to be maximal spaceable. In proving these results we have computed the dimension of L-p(Omega) for arbitrary measure spaces (Omega, Sigma, mu). The aim of the results presented here is, among others, to generalize all the previous work (since the 1960's) related to the linear structure of the sets L-p(Omega) - L-q(Omega) with q < p and L-p(Omega) - boolean OR(1 <= q<p) L-q(Omega).


Item Type:Article
Uncontrolled Keywords:Infinite measure space; lineability; spaceability; L-p-space
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:23228
Deposited On:17 Oct 2013 11:26
Last Modified:25 Nov 2016 12:32

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