A spectral theorem for bilinear compact operators in Hilbert spaces

被引：4

作者：

da Silva, Eduardo Brandani ^{[1
]}

Fernandez, Dicesar L. ^{[2
]}

de Andrade Neves, Marcus Vinicius ^{[3
]}

机构：

[1] Univ Estadual Maringa, Dept Math, Ave Colombo 5790,Campus Univ, BR-87020900 Maringa, Parana, Brazil

[2] Univ Estadual Campinas, Imecc, Rua Segio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil

[3] Univ Fed Mato Grosso, Dept Math, Av Estudantes 5055, BR-78735901 Rondonopolis, MT, Brazil

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2021年 / 15卷 / 02期

基金：

巴西圣保罗研究基金会;

关键词：

Eigenvalue; Bilinear operator; Schur representation; Spectral theorem; Hilbert space;

D O I：

10.1007/s43037-020-00119-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Current work defines Schur representation of a bilinear operator T: H x H -> H, where H is a separable Hilbert space. Introducing the concepts of self-adjoint bilinear operators, ordered eigenvalues and eigenvectors, we prove that if T is compact, self-adjoint, and its eigenvalues are ordered, then T has a Schur representation, thus obtaining a spectral theorem for T on real Hilbert spaces. We prove that the hypothesis of the existence of ordered eigenvalues is fundamental.

引用

页数：36

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