Completely contractive projections on operator algebras

David P. Blecher and Matthew Neal

Vol. 283 (2016), No. 2, 289–324

DOI: 10.2140/pjm.2016.283.289

Abstract

The main goal of this paper is to find operator algebra variants of certain deep results of Størmer, Friedman and Russo, Choi and Effros, Effros and Størmer, Robertson and Youngson, Youngson, and others, concerning projections on $C^{\ast }$-algebras and their ranges. In particular, we investigate the “bicontractive projection problem” and related questions in the category of operator algebras. To do this, we will add the ingredient of “real positivity” from recent papers of the first author with Read.

Keywords

operator algebra, completely contractive map, projection, conditional expectation, bicontractive projection, real positive, noncommutative Banach–Stone theorem

Mathematical Subject Classification 2010

Primary: 46L05, 46L07, 47L07, 47L30

Secondary: 46H10, 46B40, 46L30

Milestones

Received: 6 August 2015

Revised: 11 January 2016

Accepted: 11 January 2016

Published: 22 June 2016