POSITIVE OPERATORS ON KREIN SPACES

被引：15

作者：

ABRAMOVICH, YA ^{[1
]}

ALIPRANTIS, CD ^{[1
]}

BURKINSHAW, O ^{[1
]}

机构：

[1] INDIANA UNIV PERDUE UNIV,DEPT MATH,INDIANAPOLIS,IN 46205

来源：

ACTA APPLICANDAE MATHEMATICAE | 1992年 / 27卷 / 1-2期

关键词：

PARTIALLY ORDERED BANACH SPACE; KREIN SPACE; KREIN OPERATOR; HYPERINVARIANT SUBSPACE;

D O I：

10.1007/BF00046631

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace.

引用

页码：1 / 22

页数：22

共 19 条

[1]

BAKHTIN IA, 1962, SIB MAT ZH, V3, P156

[2]

BAKHTIN IA, 1965, MAT SBORNIK, V67, P267

[3]

BAKHTIN IA, 1964, MATH USSR SB, V64, P102

[4]

Frobenius G, 1912, SITZBER K PREUSS AKA, P456

[5]

JAMESON G, 1970, LECTURE NOTES MATH, V141

[6]

KITOVER AK, 1982, ZAP NAUCN SEM LENING, V107, P89

[7]

Krein M., 1940, DOKL AKAD NAUK SSSR, V28, P13

[8]

Krein M. G., 1948, USP MAT NAUK, V3, P3, DOI 221.238.211.53

[9]

KREIN MG, 1950, AM MATH SOC TRANSL, V26

[10]

MARKOV A., 1936, DOKL AKAD NAUK SSSR, V10, P311

← 1 2 →