RT Journal Article
T1 Distinguished subspaces of L-p of maximal dimension
A1 Botelho, Geraldo
A1 Cariello, Daniel
A1 Favaro, Vinicius V.
A1 Pellegrino, Daniel
A1 Seoane-Sepúlveda, Juan B.
AB 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).
PB Polish Acad Sciencies Inst Mathematics
SN 0039-3223
YR 2013
FD 2013
LK https://hdl.handle.net/20.500.14352/33365
UL https://hdl.handle.net/20.500.14352/33365
LA eng
NO CNPq
NO Fapemig
NO CNPq-Brazil
DS Docta Complutense
RD 4 may 2024