Distinguished subspaces of L-p of maximal dimension

作者：Botelho Geraldo^*; Cariello Daniel; Favaro Vinicius V; Pellegrino Daniel; Seoane Sepulveda Juan B

来源：Studia Mathematica, 2013, 215(3): 261-280.

DOI：10.4064/sm215-3-4

• infinite measure space
• lineability
• spaceability
• L-p-space

Let (Omega, Sigma, mu) be a measure space and 1 %26lt; p %26lt; infinity. We show that, under quite general conditions, the set L-p(Omega) - boolean OR(1 %26lt;= q%26lt;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 %26lt;= q %26lt; 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%26apos;s) related to the linear structure of the sets L-p(Omega) - L-q(Omega) with q %26lt; p and L-p(Omega) - boolean OR(1 %26lt;= q%26lt;p) L-q(Omega).

• 出版日期2013