NORMS OF VECTOR FUNCTIONALS

被引：0
|
作者：
Anoussis, M. [1 ]
Ozawa, N. [2 ]
Todorov, I. G. [3 ,4 ]
机构：
[1] Univ Aegean, Dept Math, Samos 83200, Greece
[2] Kyoto Univ, Math Sci Res Inst, Kyoto 6068502, Japan
[3] Queens Univ Belfast, Math Sci Res Ctr, Belfast BT7 1NN, Antrim, North Ireland
[4] Nankai Univ, Sch Math Sci, 94 Weijin Rd, Tianjin 300071, Peoples R China
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 05期
基金：
日本学术振兴会;
关键词：
Vector functional; von Neumann algebra; CSL algebra;
D O I：
10.1090/proc/14383
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We examine the questions of when and how the norm of a vector functional on an operator algebra can be controlled by the invariant subspace lattice of the algebra. We introduce a related operator algebraic property and show that it is satisfied by all von Neumann algebras and by all CSL algebras. We exhibit examples of operator algebras that do not satisfy the property or any scaled version of it.
引用
收藏
页码：2057 / 2068
页数：12
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