Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces

Spain, P. G. (2011) Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces. Proceedings of the Edinburgh Mathematical Society, 54(2), pp. 515-529. (doi: 10.1017/S0013091509000406)

Abstract

Palmer has shown that those hermitians in the weak-star operator closure of a commutative C*-algebra represented on a dual Banach space X that are known to commute with the initial C*-algebra form the real part of a weakly closed C*-algebra on X. Relying on a result of Murphy, it is shown in this paper that this last proviso may be dropped, and that the weak-star closure is even a W*-algebra. When the dual Banach space X is separable, one can prove a similar result for C*-equivalent algebras, via a ‘separable patch’ completion theorem for Boolean algebras of projections on such spaces.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Spain, Dr Philip
• Authors: Spain, P. G.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the Edinburgh Mathematical Society
• Publisher: Cambridge University Press
• ISSN: 0013-0915
• ISSN (Online): 1464-3839