Commutators in C*-algebras and traces

被引：0

作者：

Bikchentaev, Airat ^{[1
]}

机构：

[1] Kazan Fed Univ, 18 Kremlyovskaya Str, Kazan 420008, Russia

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2023年 / 14卷 / 02期

关键词：

Hilbert space; Linear operator; Commutator; C*-algebra; Trace; VON-NEUMANN ALGEBRA; FINITE SUMS; OPERATORS; PROJECTIONS; PRODUCTS; CONE;

D O I：

10.1007/s43034-023-00260-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let H be a Hilbert space, dimH = +infinity. Let X = U |X| be the polar decomposition of an operator X is an element of B(H). Then, X is a non-commutator if and only if both U and |X| are non-commutators. A Hermitian operator X is an element of B(H) is a commutator if and only if the Cayley transform K(X) is a commutator. Let H be a Hilbert space and dim H <= +infinity, A, B, P is an element of B(H) and P = P2. If AB = lambda B A for some lambda is an element of C\{1} then the operator AB is a commutator. The operator AP is a commutator if and only if P A is a commutator.

引用

页数：14

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