Quelques propriétés du couple d’espaces vectoriels (L¹m∕H^∞⊥, H^∞)

Jacques Chaumat

Vol. 94 (1981), No. 1, 21–45

DOI: 10.2140/pjm.1981.94.21

Abstract

Let H^∞ be a W^∗ closed subalgebra of L^∞(m) with identity. We generalize here some classical properties of the couple of linear vector spaces (L¹(m),L^∞(m)) to the couple (L¹(m)∕H^∞⊥,H^∞). We obtain, for instance, a characterization of weakly relatively compact subsets of L¹(m)∕H^∞⊥ analogous to the Dunford-Pettis theorem. To this end, we assume a legitimate hypothesis on the peak sets of H^∞.

Mathematical Subject Classification 2000

Primary: 46J15

Secondary: 46E30

Milestones

Received: 7 February 1978

Revised: 31 January 1979

Published: 1 May 1981