The dual bade theorem in locally convex spaces and reflexivity of a closed unital subalgebra

Ömer Gök

doi:10.22199/s07160917.1999.0001.00006

Abstract

The results presented in this paper extend a dual version of the reflexivity theorem of W. Bade to locally convex spaces. Dual versión of the Bade theorem in a Banach C(K)-module was firstly discovered in [1]. It is our aim to extend it to a locally convex C(K)-module. As a consequence, it is proven that each unital w* operator topology closed subalgebra of the w* operator topology closed algebra generated by a Boolean algebra of projections is reflexive.

Highlights

The results presented in this paper extend a dual version o.f the reflexivity theorem o.f W
In this artic:le, we investigate the role played by lattice order, locally convex C(K)-module and !-module in the study of operator algebras generated by Boolean algebras of projections
The study of opcrator algcbras generated by Bade complete Boolean algebras of projections in Banach spaces was firstly given by W

Summary

Introduction

The results presented in this paper extend a dual version o.f the reflexivity theorem o.f W. We let x' denote the continuous dual of a locally convex Hausdorff space Let X be a quasicomplete locally convex Hausdorff space such that /2(X) is sequentially complete and let B t:;;: /2(X) be an equicontinuous Boolcan algebra of projections. the following statements are true.

Results

Conclusion