Vol. 63, No. 2, 1976

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Weakly compact sets in H1.

Freddy Delbaen

Vol. 63 (1976), No. 2, 367–369

Suppose that A is a uniform algebra on a compact set X and that ϕ : A C is a nonzero multiplicative linear functional on A. Let Mϕ be the set of positive representing measures for ϕ. If Mϕ is finite dimensional, let m be a core measure of Mϕ. The space H1 is the closure of A in L1(m). The space H is the weak* (i.e. σ(L,L1)) closure of A in L(m). The weakly compact sets R in H1 are then those sets such that for all 𝜖 > 0 there is a bounded set in H which approximates R up to 𝜖.

Mathematical Subject Classification 2000
Primary: 46J15
Received: 4 August 1975
Published: 1 April 1976
Freddy Delbaen