Israel Journal of Mathematics

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

The normed and Banach envelopes of WeakL 1

  • Denny H. Leung


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.


Banach Lattice Finite Subset Double Sequence Lattice Homomorphism Lebesgue Measurable Function 


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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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