Completely contractive projections on operator algebras

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.Comment: To appear Pacific J Math; several corrections and small improvements. Keywords Operator algebra, completely contractive map, projection, conditional expectation, bicontractive projection, real positive, noncommutative Banach-Stone theore

Metric characterizations II

The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces, operator systems, operator algebras, and so on), in terms which are purely linear-metric, by which we mean that they only use the vector space structure of the space and its matrix norms. In the last part we give some characterizations of operator algebras (which are not linear-metric in our strict sense described in the paper).Comment: Presented at the AMS/SAMS Satellite Conference on Abstract Analysis, University of Pretoria, South Africa, 5-7 December 2011. Revision of 2/24/2012 (Examples after theorem 3.2 added