The Normed and Banach Envelopes of Weakl
نویسنده
چکیده
is finite, where λ denotes Lebesgue measure. Let ρ be the gauge functional of the convex hull of the unit ball {f : q(f) ≤ 1} of the quasi-norm q, and let N be the null space of ρ. The normed envelope of WeakL, which we denote by W , is the space (WeakL/N, ρ). The Banach envelope of WeakL, W , is the completion of W . We show that W is isometrically lattice isomorphic to a sublattice of W . It is also shown that all rearrangement invariant Banach function spaces are isometrically lattice isomorphic to a sublattice of W .
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