Geometry of the unit ball and representation theory for operator algebras

Elias G. Katsoulis

Vol. 216 (2004), No. 2, 267–292

DOI: 10.2140/pjm.2004.216.267

Abstract

We investigate the relationship between the facial structure of the unit ball of an operator algebra 𝒜 and its algebraic structure, including the hereditary subalgebras and the socle of 𝒜. Many questions about the facial structure of 𝒜 are studied with the aid of representation theory. For that purpose we establish the existence of reduced atomic type representations for certain nonselfadjoint operator algebras. Our results are applicable to C^∗-algebras, strongly maximal TAF algebras, free semigroup algebras and various semicrossed products.

Milestones

Received: 3 June 2002

Revised: 19 November 2003

Published: 1 October 2004