location:  Publications → journals → CJM
Abstract view

# Unperforated Pairs of Operator Spaces and Hyperrigidity of Operator Systems

Published:2018-03-22
Printed: Dec 2018
• Raphaël Clouâtre,
Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2, Manitoba
 Format: LaTeX MathJax PDF

## Abstract

We study restriction and extension properties for states on C$^*$-algebras with an eye towards hyperrigidity of operator systems. We use these ideas to provide supporting evidence for Arveson's hyperrigidity conjecture. Prompted by various characterizations of hyperrigidity in terms of states, we examine unperforated pairs of self-adjoint subspaces in a C$^*$-algebra. The configuration of the subspaces forming an unperforated pair is in some sense compatible with the order structure of the ambient C$^*$-algebra. We prove that commuting pairs are unperforated, and obtain consequences for hyperrigidity. Finally, by exploiting recent advances in the tensor theory of operator systems, we show how the weak expectation property can serve as a flexible relaxation of the notion of unperforated pairs.
 Keywords: operator system, state, peak point, hyperrigidity conjecture
 MSC Classifications: 46L07 - Operator spaces and completely bounded maps [See also 47L25] 46L30 - States 46L52 - Noncommutative function spaces

 top of page | contact us | privacy | site map |