Let C be a conjugation on a separable complex Hilbert space H.An operator T on H is said to be C-symmetric if CTC=-T^(*),and T is said to be Cskew symmetric if CTC=-T^(*).It is proved in this paper that each C-skew sy...Let C be a conjugation on a separable complex Hilbert space H.An operator T on H is said to be C-symmetric if CTC=-T^(*),and T is said to be Cskew symmetric if CTC=-T^(*).It is proved in this paper that each C-skew symmetric operator can be written as the sum of two commutators of C-symmetric operators.展开更多
For a conjugation C on a separable,complex Hilbert space H,the set S_(C) of Csymmetric operators on H forms a weakly closed,selfadjoint,Jordan operator algebra.In this paper,the authors study S_(C) in comparison with ...For a conjugation C on a separable,complex Hilbert space H,the set S_(C) of Csymmetric operators on H forms a weakly closed,selfadjoint,Jordan operator algebra.In this paper,the authors study S_(C) in comparison with the algebra B(H)of all bounded linear operators on H,and obtain S_(C)-analogues of some classical results concerning B(H).The authors determine the Jordan ideals of S_(C) and their dual spaces.Jordan automorphisms of S_(C) are classified.The authors determine the spectra of Jordan multiplication operators on S_(C) and their different parts.It is proved that those Jordan invertible ones constitute a dense,path connected subset of S_(C).展开更多
In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators t...In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same.Also,some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.展开更多
An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conju...An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conjugate normality under similarity.Given an operator T,we prove that every operator A similar to T is conjugate normal if and only if there exist complex numbersλ_(1),λ_(2)such that(T-λ_(1))(T-λ_(2))=0.展开更多
基金partly supported by the National Natural Science Foundation of China(Grant No.12i7195)by the National Key R&D Program(Grant No.2020YFA0714101).
文摘Let C be a conjugation on a separable complex Hilbert space H.An operator T on H is said to be C-symmetric if CTC=-T^(*),and T is said to be Cskew symmetric if CTC=-T^(*).It is proved in this paper that each C-skew symmetric operator can be written as the sum of two commutators of C-symmetric operators.
基金supported by the National Natural Science Foundation of China(Nos.12401149,12171195)the National Key Research and Development Program of China(No.2020YFA0714101).
文摘For a conjugation C on a separable,complex Hilbert space H,the set S_(C) of Csymmetric operators on H forms a weakly closed,selfadjoint,Jordan operator algebra.In this paper,the authors study S_(C) in comparison with the algebra B(H)of all bounded linear operators on H,and obtain S_(C)-analogues of some classical results concerning B(H).The authors determine the Jordan ideals of S_(C) and their dual spaces.Jordan automorphisms of S_(C) are classified.The authors determine the spectra of Jordan multiplication operators on S_(C) and their different parts.It is proved that those Jordan invertible ones constitute a dense,path connected subset of S_(C).
基金supported in part by the National Natural Science Foundation of China(11201331,11771323)。
文摘In this article,we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables.Surprisingly,the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same.Also,some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.
基金supported by the National Natural Science Foundation of China (Grant No.12171195).
文摘An operator T on a separable,infinite dimensional,complex Hilbert space H is called conjugate normal if C|T|C=|T^(*)| for some conjugate linear,isometric involution C on H.This paper focuses on the invariance of conjugate normality under similarity.Given an operator T,we prove that every operator A similar to T is conjugate normal if and only if there exist complex numbersλ_(1),λ_(2)such that(T-λ_(1))(T-λ_(2))=0.
