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Some stability properties of Arens regular bilinear operators

Published online by Cambridge University Press:  20 January 2009

A. Ülger
A. Ülger
Affiliation:
Department of MathematicsBoǧaziçi University80815 Bebek, IstanbulTurkey
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Abstract

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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 3 , October 1991 , pp. 443 - 454
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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