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.
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页数：28
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