Quasi Hyperrigidity and Weak Peak Points for Non-Commutative Operator Systems
Operator Algebras
2016-10-10 v1
Abstract
In this article, we introduce the notions of weak boundary repre- sentation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in C* algebras. An analogue of Saskin theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of C* algebras is proved. We also show that, if an irreducible representation is a weak boundary representation and weak peak then it is a boundary repre- sentation. Several examples are provided to illustrate these notions. It is also observed that isometries on Hilbert spaces play an important role in the study of certain operator systems.
Cite
@article{arxiv.1610.02165,
title = {Quasi Hyperrigidity and Weak Peak Points for Non-Commutative Operator Systems},
author = {M. N. N. Namboodiri and S. Pramod and P. Shankar and A. K. Vijayarajan},
journal= {arXiv preprint arXiv:1610.02165},
year = {2016}
}