Bilinear operators on L^∞(G) of locally compact groups

Colin C. Graham and Anthony To-Ming Lau

Vol. 158 (1993), No. 1, 157–176

DOI: 10.2140/pjm.1993.158.157

Abstract

Let G and H be compact groups. We study in this paper the space Bil^σ = Bil^σ(L^∞(G), L^∞(H)). That space consists of all bounded bilinear functionals on L^∞(G) × L^∞(H) that are weak^∗ continuous in each variable separately. We prove, among other things, that Bil^σ is isometrically isomorphic to a closed two-sided ideal in BM(G,H). In the case of abelian G, H, we show that Bil^σ does not have an approximate identity and that G ×H is dense in the maximal ideal space of Bil^σ. Related results are given.

Mathematical Subject Classification 2000

Primary: 43A15

Secondary: 47B38

Milestones

Received: 30 October 1990

Revised: 1 February 1992

Published: 1 March 1993