On linear maps preserving complex symmetry

被引：4

作者：

Ji, Youqing ^{[1
]}

Liu, Ting ^{[2
]}

Zhu, Sen ^{[1
]}

机构：

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

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 468卷 / 02期

基金：

美国国家科学基金会;

关键词：

Complex symmetric operator; Linear preserver; Similarity; Completely positive map; UNITARY EQUIVALENCE; OPERATORS; MATRIX;

D O I：

10.1016/j.jmaa.2018.09.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An operator T on a complex Hilbert space H is said to be complex symmetric if there exists a conjugate-linear, isometric involution C : H -> H so that CTC = T*. This paper is devoted to describing which linear maps leave the class of complex symmetric operators invariant. Complete characterizations are obtained for several classes of linear maps, including similarity transformations, surjective linear isometries, multiplication operators and certain completely positive maps. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1144 / 1163

页数：20

共 18 条

[1]

Balayan L, 2010, OPER MATRICES, V4, P53

[2] Complex symmetric operators and applications [J].

Garcia, SR ;

Putinar, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (03) :1285-1315

[3] Complex symmetric operators and applications II [J].

Garcia, Stephan Ramon ;

Putinar, Mihai .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (08) :3913-3931

[4] Mathematical and physical aspects of complex symmetric operators [J].

Garcia, Stephan Ramon ;

Prodan, Emil ;

Putinar, Mihai .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (35)

[5]

Garcia SR, 2012, J OPERAT THEOR, V68, P179

[6] UNITARY EQUIVALENCE TO A COMPLEX SYMMETRIC MATRIX: A MODULUS CRITERION [J].

Garcia, Stephan Ramon ;

Poore, Daniel E. ;

Wyse, Madeline K. .

OPERATORS AND MATRICES, 2011, 5 (02) :273-287

[7] SOME NEW CLASSES OF COMPLEX SYMMETRIC OPERATORS [J].

Garcia, Stephan Ramon ;

Wogen, Warren R. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 362 (11) :6065-6077

[8] Complex symmetric partial isometries [J].

Garcia, Stephan Ramon ;

Wogen, Warren R. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2009, 257 (04) :1251-1260

[9] A C*-ALGEBRA APPROACH TO COMPLEX SYMMETRIC OPERATORS [J].

Guo, Kunyu ;

Ji, Youqing ;

Zhu, Sen .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 367 (10) :6903-6942

[10] Some general techniques on linear preserver problems [J].

Guterman, A ;

Li, CK ;

Semrl, P .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 315 (1-3) :61-81

← 1 2 →