Closed operators in semi-Hilbertian spaces

被引：12

作者：

Baklouti, Hamadi ^{[1
]}

Namouri, Sirine ^{[1
]}

机构：

[1] Sfax Univ, Fac Sci Sfax, Sfax, Tunisia

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 20期

关键词：

Semi-Hilbertian space; closed operator; relatively bounded operator; adjoint of an operator;

D O I：

10.1080/03081087.2021.1932709

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a positive operator A on a Hilbert space, we introduce the notion of an A-closed linear operator as a natural extension of the usual notion of an A-bounded operator. We summarize a number of results and examples about this class of operators. We show that all A-bounded operators are A-closed and we prove that the class of A-closed operators is stable under perturbation by A-bounded operators. Moreover, we give sufficient conditions for the adjoint operator T * to be A-closed when T is A-closed. This study is motivated by recent developments of pseudo-Hermitian quantum mechanics.

引用

页码：5847 / 5858

页数：12

共 12 条

[1] The Moore-Penrose Pseudoinverse: A Tutorial Review of the Theory [J].