scholarly journals The g-Drazin inverses of special operator matrices

2021 ◽  
pp. 151-162
Author(s):  
Huan in Chen ◽  
Marjan Sheibani Abdolyousefi
Keyword(s):  
Operator Matrices ◽  
Special Operator

scholarly journals The convex properties and norm bounds for operator matrices involving contractions

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1271-1281
Author(s):  
Yuan Li ◽  
Mengqian Cui ◽  
Shasha Hu
Keyword(s):  
Hilbert Space ◽  
Compact Set ◽  
Operator Matrices ◽  
Infinite Dimensional ◽  
Special Operator

In this note, the norm bounds and convex properties of special operator matrices ~H(m)n and ~S(m)n are investigated. When Hilbert space K is infinite dimensional, we firstly show that ~H(m)n = ~H(m)n+1 and ~S(m) n = ~S(m)n+1, for m, n = 1,2,.... Then we get that ~H(m) n is a convex and compact set in the ?* topology. Moreover, some norm bounds for ~H(m) n and ~S(m)n are given.

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

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

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