The orthogonal Lie algebra of operators: Ideals and derivations

被引：4

作者：

Bu, Qinggang ^{[1
]}

Zhu, Sen ^{[2
]}

机构：

[1] Jilin Univ, Inst Math, Changchun 130012, Peoples R China

[2] Jilin Univ, Dept Math, Changchun 130012, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 489卷 / 01期

基金：

美国国家科学基金会;

关键词：

Orthogonal Lie algebra; Lie ideal; Derivation; Skew-symmetric operator; Skew-symmetric matrix; SYMMETRIC-OPERATORS; AUTOMORPHIC-FUNCTIONS; SKEW; DECOMPOSITION;

D O I：

10.1016/j.jmaa.2020.124134

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study in this paper the infinite-dimensional orthogonal Lie algebra O-C which consists of all bounded linear operators Ton a separable, infinite-dimensional, complex Hilbert space Hsatisfying CTC=-T*, where C is a conjugation on H. By employing results from the theory of complex symmetric operators and skew-symmetric operators, we determine the Lie ideals of O-C and their dual spaces. We study derivations of O-C and determine their spectra. These results complete some results of P. de la Harpe and provide interesting contrasts between O-C and the algebra B(H) of all bounded linear operators on H. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：28

共 50 条

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