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Israel Journal of Mathematics

, Volume 121, Issue 1, pp 247–264 | Cite as

The normed and Banach envelopes of WeakL 1

  • Denny H. Leung
Article

Abstract

The space WeakL 1 consists of all Lebesgue measurable functions on [0,1] such thatq(f)=supcλ{t:|f(t)|>c} c>0 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-normq, and letN be the null space of ρ. The normed envelope of WeakL 1, which we denote byW, is the space (WeakL 1/N, ρ). The Banach envelope of WeakL 1,\(\overline W \), is the completion ofW. We show that\(\overline W \) is isometrically lattice isomorphic to a sublattice ofW. It is also shown that all rearrangement invariant Banach function spaces are isometrically lattice isomorphic to a sublattice ofW.

Keywords

Banach Lattice Finite Subset Double Sequence Lattice Homomorphism Lebesgue Measurable Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 2001

Authors and Affiliations

  • Denny H. Leung
    • 1
  1. 1.Department of MathematicsNational University of SingaporeSingapore

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