Completely contractive projections on operator algebras

TL;DR

This paper explores the structure of completely contractive projections on operator algebras, extending classical results on projections in C*-algebras by incorporating real positivity concepts.

Contribution

It introduces operator algebra variants of classical projection results, focusing on the bicontractive projection problem and utilizing real positivity techniques.

Findings

Characterization of projections with specific contractivity properties

Extension of classical C*-algebra projection results to operator algebras

Application of real positivity to analyze projections

Abstract

The main goal of this paper is to find operator algebra variants of certain deep results of Stormer, Friedman and Russo, Choi and Effros, Effros and Stormer, Robertson and Youngson, Youngson, and others, concerning projections on C*-algebras and their ranges. (See papers of these authors referenced in the bibliography.) 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.