The inverse of two-level Toeplitz operator matrices

The inverse of nonsymmetric two-level Toeplitz operator matrices

Linear Algebra and its Applications ◽

10.1016/j.laa.2012.04.048 ◽

2012 ◽

Vol 437 (9) ◽

pp. 2142-2158

Author(s):

Selcuk Koyuncu ◽

Hugo J. Woerdeman

Keyword(s):

Toeplitz Operator ◽

Operator Matrices

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Local Spectral Properties Under Conjugations

Mediterranean Journal of Mathematics ◽

10.1007/s00009-021-01731-7 ◽

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.

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Hyponormality of Toeplitz operators with non-harmonic symbols on the Bergman spaces

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02602-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Sumin Kim ◽

Jongrak Lee

Keyword(s):

Toeplitz Operator ◽

Bergman Space ◽

Toeplitz Operators ◽

Bergman Spaces ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Necessary And Sufficient

AbstractIn this paper, we present some necessary and sufficient conditions for the hyponormality of Toeplitz operator $T_{\varphi }$ T φ on the Bergman space $A^{2}(\mathbb{D})$ A 2 ( D ) with non-harmonic symbols under certain assumptions.

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