Abstract
In this paper we present three results about Arens regular bilinear operators. These are: (a). Let X, Y be two Banach spaces, K a compact Hausdorff space, µ a Borel measure on K and m: X × Y →ℂ a bounded bilinear operator. Then the bilinear operator defined by is regular iff m is regular, (b) Let (Xα), (Xα),(Zα) be three families of Banach spaces and let mα:Xα ×Yα→Zα, be a family of bilinear operators with supα∥mα∥<∞. Then the bilinear operator defined by is regular iff each mα, is regular, (c) Let X, Y have the Dieudonné property and let m:X × Y→Z be a bounded bilinear operator with m(X×Y) separable and such that, for each z′ in ext Z′1, z′∘m is regular. Then m is regular. Several applications of these results are also given.
Publisher
Cambridge University Press (CUP)
Reference26 articles.
1. Periodicity of functionals and representations of normed algebras on reflexive spaces
2. On weakly compact operators from some uniform algebras
3. Arens regularity of the algebra C(K, A);Ülcer;J. London Math. Soc.,1990
4. Extreme points in duals of operator spaces
5. 19. Phelps R. P. , Integral representations for elements of convex sets, in Studies in Functional Analysis (MAA Studies in Mathematics 21, edited by R. G. Bartle.