The normed and Banach envelopes of Weak L^1
泛函分析
2007-05-23 v1
摘要
The space Weak L^1 consists of all measurable functions on [0,1] such that q(f) = sup_{c>0} c \lambda{t : |f(t)| > c} is finite, where \lambda denotes Lebesgue measure. Let \rho be the gauge functional of the unit ball {f : q(f) \leq 1} of the quasi- norm q, and let N be the null space of \rho. The normed envelope of Weak L^1, which we denote by W, is the space (Weak L^1/N, \rho). The Banach envelope of Weak L^1, \overline{W}, is the completion of W. We show that \overline{W} is isometrically lattice isomorphic to a sublattice of W. It is also shown that all rearrangement invariant Banach function spaces are isometrically isomorphic to a sublattice of W.
引用
@article{arxiv.math/9806009,
title = {The normed and Banach envelopes of Weak L^1},
author = {Denny H. Leung},
journal= {arXiv preprint arXiv:math/9806009},
year = {2007}
}