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Rearrangement Invariant Continuous Linear Functionals on Weak L1

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Abstract

We show that in the dual of Weak L1 the subspace of all rearrangement invariant continuous linear functionals is lattice isometric to a space L1(μ) and is the linear hull of the maximal elements of the dual unit ball. We also show that the dual of Weak L1 contains a norm closed weak* dense ideal which is lattice isometric to an ℓ1-sum of spaces of type C(K).

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801

    Heinrich P. Lotz

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  1. Heinrich P. Lotz
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Correspondence to Heinrich P. Lotz.

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Helmut H. Schaefer in memoriam

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Lotz, H.P. Rearrangement Invariant Continuous Linear Functionals on Weak L1. Positivity 12, 119–132 (2008). https://doi.org/10.1007/s11117-007-2111-9

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  • DOI: https://doi.org/10.1007/s11117-007-2111-9

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