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Completely contractive representations of some doubly generated antisymmetric operator algebras.

Power, Stephen C. (1998) Completely contractive representations of some doubly generated antisymmetric operator algebras. Proceedings of the American Mathematical Society, 126 (8). pp. 2355-2359. ISSN 1088-6826

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Abstract

Contractive weak star continuous representations of the Fourier binest algebra (of Katavolos and Power) are shown to be completely contractive. The proof depends on the approximation of by semicrossed product algebras and on the complete contractivity of contractive representations of such algebras. The latter result is obtained by two applications of the Sz.-Nagy-Foias lifting theorem. In the presence of an approximate identity of compact operators it is shown that an automorphism of a general weakly closed operator algebra is necessarily continuous for the weak star topology and leaves invariant the subalgebra of compact operators. This fact and the main result are used to show that isometric automorphisms of the Fourier binest algebra are unitarily implemented.

Item Type: Article
Journal or Publication Title: Proceedings of the American Mathematical Society
Additional Information: First published in Proceedings of the American Mathematical Society 126, (8), published by the American Mathematical Society.
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19439
Deposited By: ep_ss_importer
Deposited On: 18 Nov 2008 12:31
Refereed?: Yes
Published?: Published
Last Modified: 10 Dec 2016 01:17
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19439

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