ON ∞-COMPLEX SYMMETRIC OPERATORS

2017 ◽  
Vol 60 (1) ◽  
pp. 35-50
Author(s):  
MUNEO CHŌ ◽  
EUNGIL KO ◽  
JI EUN LEE
Keyword(s):  
Spectral Properties ◽  
Symmetric Operator ◽  
Complex Symmetric Operator ◽  
Decomposition Property ◽  
Complex Symmetric ◽  
Symmetric Operators

AbstractIn this paper, we study spectral properties and local spectral properties of ∞-complex symmetric operators T. In particular, we prove that if T is an ∞-complex symmetric operator, then T has the decomposition property (δ) if and only if T is decomposable. Moreover, we show that if T and S are ∞-complex symmetric operators, then so is T ⊗ S.

scholarly journals Perturbation of the spectra of complex symmetric operators

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 191-199
Author(s):  
Qinggang Bu ◽  
Cun Wang
Keyword(s):  
Hilbert Space ◽  
Symmetric Operator ◽  
Separable Hilbert Space ◽  
Symmetric Matrix ◽  
Compact Perturbation ◽  
Complex Symmetric Operator ◽  
Single Valued Extension Property ◽  
Complex Symmetric ◽  
Symmetric Operators ◽  
Complex Separable Hilbert Space

An operator T on a complex Hilbert space H is called complex symmetric if T has a symmetric matrix representation relative to some orthonormal basis for H. This paper focuses on the perturbation theory for the spectra of complex symmetric operators. We prove that each complex symmetric operator on a complex separable Hilbert space has a small compact perturbation being complex symmetric and having the single-valued extension property. Also it is proved that each complex symmetric operator on a complex separable Hilbert space has a small compact perturbation being complex symmetric and satisfying generalized Weyl?s theorem.

scholarly journals On power similarity of complex symmetric operators

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3577-3586
Author(s):  
Eungil Ko ◽  
Ji Lee ◽  
Mee-Jung Lee
Keyword(s):  
Symmetric Operator ◽  
Complex Symmetric Operator ◽  
Closed Set ◽  
Complex Symmetric ◽  
Symmetric Operators

In this paper, we study properties of operators which are power similar to complex symmetric operators. In particular, we prove that if T is power similar to a complex symmetric operator, then T is decomposable modulo a closed set S ? C if and only if R has the Bishop?s property (?) modulo S. Using the results, we get some applications of such operators.

scholarly journals Skew m-complex symmetric operators

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 2975-2983
Author(s):  
Muneo Chō ◽  
Eungil Ko ◽  
Ji Lee
Keyword(s):  
Symmetric Operator ◽  
Complex Symmetric Operator ◽  
Complex Symmetric ◽  
Symmetric Operators

In this paper we study skew m-complex symmetric operators. In particular, we show that if T ? L(H) is a skew m-complex symmetric operator with a conjugation C, then eitT , e-itT , and e-itT* are (m,C)-isometric for every t ? R. Moreover, we examine some conditions for skew m-complex symmetric operators to be skew (m-1)-complex symmetric.

scholarly journals Local Spectral Properties Under Conjugations

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Pietro Aiena ◽  
Fabio Burderi ◽  
Salvatore Triolo
Keyword(s):  
Hilbert Space ◽  
Spectral Properties ◽  
Operator Matrices ◽  
Weyl Type Theorems ◽  
Triangular Operator ◽  
Analytic Core ◽  
Complex Symmetric ◽  
Symmetric Operators ◽  
The Relationship

AbstractIn this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and $$T\in L(H)$$ T ∈ L ( H ) . We also study the relationship between the quasi-nilpotent part of the adjoint $$T^*$$ T ∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form $$JT^*J$$ J T ∗ J . The theory is exemplified in some concrete cases.

scholarly journals On complex symmetric operator matrices

2013 ◽  
Vol 406 (2) ◽  
pp. 373-385 ◽  
Author(s):  
Sungeun Jung ◽  
Eungil Ko ◽  
Ji Eun Lee
Keyword(s):  
Symmetric Operator ◽  
Operator Matrices ◽  
Complex Symmetric Operator ◽  
Complex Symmetric

scholarly journals On symmetric and skew-symmetric operators

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 293-303 ◽  
Author(s):  
Chafiq Benhida ◽  
Muneo Chō ◽  
Eungil Ko ◽  
Ji Lee
Keyword(s):  
Spectral Properties ◽  
Complex Symmetric ◽  
Symmetric Operators

In this paper we show many spectral properties that are inherited by m-complex symmetric and m-skew complex symmetric operators and give new results or recapture some known ones for complex symmetric operators.

Weyl type theorems for complex symmetric operator matrices

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2891-2900 ◽  
Author(s):  
Il An ◽  
Eungil Ko ◽  
Ji Lee
Keyword(s):  
Symmetric Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Operator Matrices ◽  
Complex Symmetric Operator ◽  
Weyl Type Theorems ◽  
Complex Symmetric ◽  
Necessary And Sufficient

In this paper, we study Weyl type theorems for complex symmetric operator matrices. In particular, we give a necessary and sufficient condition for complex symmetric operator matrices to satisfy a-Weyl?s theorem. Moreover, we also provide the conditions for such operator matrices to satisfy generalized a-Weyl?s theorem and generalized a-Browder?s theorem, respectively. As some applications, we give various examples of such operator matrices which satisfy Weyl type theorems.

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