On lifting of operators to Hilbert spaces induced by positive selfadjoint operators

被引：14

作者：

Cojuhari, P

Gheondea, A ^{[1
]}

机构：

[1] Bilkent Univ, Dept Math, TR-06800 Ankara, Turkey

[2] Acad Romane, Inst Matemat, Bucharest 70700, Romania

[3] AGH Univ Sci & Technol, Dept Appl Math, PL-30059 Krakow, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2005年 / 304卷 / 02期

关键词：

energy space; induced Hilbert space; lifting of operators; boundary value problems; spectrum;

D O I：

10.1016/j.jmaa.2004.09.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of induced Hilbert spaces for positive unbounded operators and show that the energy spaces associated to several classical boundary value problems for partial differential operators are relevant examples of this type. The main result is a generalization of the Krein-Reid lifting theorem to this unbounded case and we indicate how it provides estimates of the spectra of operators with respect to energy spaces. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：584 / 598

页数：15

共 16 条

[1]

BRUDNYI YA, 1986, ITOGI NAUKI TEKHN MA, V24, P3

[2]

DIEUDONNE J., 1961, P INT S LIN SPAC JER, P115

[3] Spectral theories of semi-restricted operators and its application in the spectral decomposition of differential operators. Second chapter. [J].