Browder spectra and essential spectra of operator matrices

Zhang, Yun Nan; Zhong, Huai Jie; Li, Lin

doi:10.1007/s10114-007-6339-x

Cited by 15 publications

(5 citation statements)

References 7 publications

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“…If there exists a non-zero complex polynomial P (z) such that P (T ) is Riesz then we say that T ∈ B(X) is polynomially Riesz, these operators have been discussed in [6] and [10]. It is useful to mention that for T ∈ B(X) and (M, N ) ∈ Red(T ) ( [10], [12]):…”

Section: Introductionmentioning

confidence: 99%

Generalized Drazin-Riesz invertibility for operator matrices

2020

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Let A ∈ B(X), B ∈ B(Y ) and C ∈ B(Y, X) where X and Y are infinite Banach or Hilbert spaces. Let M C =A C 0 B be 2 × 2 upper triangular operator matrix acting on X ⊕ Y . In this paper, we consider some necessary and sufficient conditions for M C to be generalized Drazin-Riesz invertible. Furthermore, the set C∈B(Y,X) σ gDR (M C ) will be investigated and their relation between C∈B(Y,X) σ b (M C ) will be studied, where σ gDR (M C ) and σ b (M C ) denote the generalized Drazin-Riesz spectrum and the Browder spectrum, respectively.2010 Mathematics Subject Classification. 47A10, 47A53.

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Section: Introductionmentioning

confidence: 99%

Generalized Drazin-Riesz invertibility for operator matrices

2020

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“…(1.1) defined on the separable Hilbert space H ⊕ K. Recall that the problem of the relationship between the spectrum, various distinguished parts of the spectrum of an upper triangular and Drazin invertibility and its diagonal has been considered by a number of authors in the recent past, we can see [4,5,13,21,22,[28][29][30] and the references therein for recent reviews on this topic. A related, and seemingly more demanding, problem is the following.…”

Section: Introductionmentioning

confidence: 99%

Left and Right Generalized Drazin Invertibility of an Upper Triangular Operator Matrices with Application to Boundary Value Problems

Hocine¹,

Messirdi²,

Benharrat

2019

ijaa

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In this paper we investigate the quasi-nilpotent part and the analytical core for the upper triangular operator matrix M C in terms of those of A and B. We give some necessary and sufficient conditions for M C to be left or right generalized Drazin invertible operator for some C ∈ B(K, H). As an application, we study the existence and uniqueness of the solution for abstract boundary value problems described by upper triangular operator matrices with right generalized Drazin invertible component.

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“…In [16], authors investigate the filling-in-holes problem of 2 × 2 upper triangular operator matrices for Browder spectrum, they showed the following theorem.…”

Section: Introductionmentioning

confidence: 99%

Limit Points for Browder Spectrum of Operator Matrices

Tajmouati¹,

Karmouni²,

Chrifi³

2018

Preprint

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Let A ∈ B(X) and B ∈ B(Y ), where X and Y are Banach spaces, and let M C be an operator acting on X ⊕ Y given by M C = A C 0 B . We investigate the limit point set of the Browder spectrum of M C . It is shown that accσ b (M C ) ∪ Waccσ b = accσ b (A) ∪ accσ b (B) where Waccσ b is a subsets of accσ * (B) ∩ accσ * (A) and a union of certain holes in accσ b (M C ). Furthermore, several sufficient conditions for accσ b (M C ) = accσ b (A) ∪ accσ b (B) holds for every C ∈ B(Y, X) are given. 2010 Mathematics Subject Classification. 47A10, 47A11.

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Browder spectra and essential spectra of operator matrices

Cited by 15 publications

References 7 publications

Generalized Drazin-Riesz invertibility for operator matrices

Generalized Drazin-Riesz invertibility for operator matrices

Left and Right Generalized Drazin Invertibility of an Upper Triangular Operator Matrices with Application to Boundary Value Problems

Limit Points for Browder Spectrum of Operator Matrices

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