Positive Decompositions of Selfadjoint Operators

被引：0
作者：
Guillermina Fongi
Alejandra Maestripieri
机构：
[1] Universidad de Buenos Aires,Departamento de Matemática, Facultad de Ciencias Exactasy Naturales
[2] Instituto Argentino de Matemática-CONICET,Departamento de Matemática, Facultad de Ingeniería
[3] Universisdad de Buenos Aires,undefined
来源：
Integral Equations and Operator Theory | 2010年 / 67卷
关键词：
47B15; 58B20; Selfadjoint operators; congruence of operators; indefinite metric spaces;
D O I：
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学科分类号：
摘要：
Given a linear bounded selfadjoint operator a on a complex separable Hilbert space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{H}}$$\end{document}, we study the decompositions of a as a difference of two positive operators whose ranges satisfy an angle condition. These decompositions are related to the canonical decompositions of the indefinite metric space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(\mathcal{H},\langle\,, \,\rangle_a)}$$\end{document}, associated to a. As an application, we characterize the orbit of congruence of a in terms of its positive decompositions.
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页码：109 / 121
页数：12
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