The normed and Banach envelopes of Weak L^1
| dc.creator | Leung, Denny H. | |
| dc.date | 1998-06-03 | |
| dc.date.accessioned | 2026-07-07T06:32:58Z | |
| dc.date.available | 2026-07-07T06:32:58Z | |
| dc.description | The space Weak L^1 consists of all measurable functions on [0,1] such that q(f) = sup_{c>0} c λ{t : |f(t)| > c} is finite, where λdenotes Lebesgue measure. Let ρbe 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 ρ. The normed envelope of Weak L^1, which we denote by W, is the space (Weak L^1/N, ρ). 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. | |
| dc.identifier | https://arxiv.org/abs/math/9806009 | |
| dc.identifier | http://arxiv.org/abs/math/9806009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99040 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46E30, 46B42, 46B40 | |
| dc.title | The normed and Banach envelopes of Weak L^1 | |
| dc.type | text |