scholarly journals The class of complex symmetric operators is not norm closed

2012 ◽  
Vol 140 (5) ◽  
pp. 1705-1708 ◽  
Author(s):  
Sen Zhu ◽  
Chun Guang Li ◽  
You Qing Ji
Keyword(s):  
Complex Symmetric ◽  
Symmetric Operators

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.

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 Reducible and irreducible approximation of complex symmetric operators

2019 ◽  
Vol 100 (1) ◽  
pp. 341-360 ◽  
Author(s):  
Ting Liu ◽  
Jiayin Zhao ◽  
Sen Zhu
Keyword(s):  
Complex Symmetric ◽  
Symmetric Operators

scholarly journals Complex symmetric operators and applications

2005 ◽  
Vol 358 (03) ◽  
pp. 1285-1315 ◽  
Author(s):  
Stephan Ramon Garcia ◽  
Mihai Putinar
Keyword(s):  
Complex Symmetric ◽  
Symmetric Operators

Remarks on the Structure of Complex Symmetric Operators

2007 ◽  
Vol 59 (4) ◽  
pp. 585-590 ◽  
Author(s):  
T. M. Gilbreath ◽  
Warren R. Wogen
Keyword(s):  
Complex Symmetric ◽  
Symmetric Operators
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