On weak boundary representations and quasi hyperrigidity for operator systems

被引：1

作者：

Arunkumar, C. S. ^{[1
]}

Vijayarajan, A. K. ^{[1
]}

机构：

[1] Kerala Sch Math, Calicut 673571, Kerala, India

来源：

JOURNAL OF ANALYSIS | 2022年 / 30卷 / 03期

关键词：

Operator system; Completely positive map; Weak unique extension property; Weak boundary representation; Quasi hyperrigid sets; TENSOR-PRODUCTS;

D O I：

10.1007/s41478-022-00405-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A be a unital C-*-algebra and S be an operator system in A. It is shown that, an irreducible representation pi of A is a weak boundary representation for S if and only if its n-amplification pi((n)) is a weak boundary representation for the operator system M-n(S)for any n >= 2. Also, we deduce that the operator system S is quasi hyperrigid in A if and only if the operator system M-n(S) is quasi hyperrigid in M-n(A) any n >= 2.

引用

页码：1219 / 1227

页数：9

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