Weyl’s theorem for upper triangular operator matrices

Cao, X.; Guo, Maozheng; Meng, Bo

doi:10.1016/j.laa.2004.12.005

Cited by 16 publications

(9 citation statements)

References 9 publications

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“…A study of the spectrum, the Browder and Weyl spectra, and the Browder and Weyl theorems for the operator M C , and the related diagonal operator M 0 = A ⊕ B, has been carried out by a number of authors in the recent past (see [12,19]). Thus, if either S(A It is known from [5,11,12]…”

Section: Notation and Terminologymentioning

confidence: 99%

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Generalized Weyl’s theorem and property (gw) for upper triangular operator matrices

Rashid

2018

Arab. J. Math.

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It is known that if A ∈ L (X) and B ∈ L (Y) are Banach operators with the single-valued extension property, SVEP, then the matrix operator M C = A C 0 B has SVEP for every operator C ∈ L (Y , X), and hence obeys generalized Browder's theorem. This paper considers conditions on operators A, B, and M 0 ensuring generalized Weyl's theorem and property (Bw) for operators M C. Moreover, certain conditions are explored on Banach space operators T and S so that T ⊕ S obeys property (gw).

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Section: Notation and Terminologymentioning

confidence: 99%

“…Again, if σ a (A * ) has empty interior, A is an a-isoloid (isolated points of σ a (A) are eigenvalues of A) and A ∈ aW, then M 0 ∈ aW ⇒ M C ∈ aW [11,Theorem 3.3].…”

Section: Notation and Terminologymentioning

confidence: 99%

Generalized Weyl’s theorem and property (gw) for upper triangular operator matrices

Rashid

2018

Arab. J. Math.

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“…We collect in the following proposition some useful spectral properties of M C from [5,21,9,11], which can be easily checked. …”

Section: Preliminariesmentioning

confidence: 99%

“…In the recent past, there are numerous publications considering spectral properties of 2 × 2 upper triangular operator matrices. See, for example, [14,10,2,8,5,17]. It is wroth mentioning that the authors, applying local spectral theory, estimate the set (σ * (A) ∪ σ * (B))\σ * (M C ) and obtain some sufficient conditions of…”

Section: Introductionmentioning

confidence: 99%

Weyl type theorems of 2×2 upper triangular operator matrices

Bai

Huang

Chen

2016

Journal of Mathematical Analysis and Applications

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“…Those spectra of M C which satisfy equation (10), (11), (12), respectively, are called to have the filling-in-hole property, generalized filling-in-hole property, convex filling-in-hole property, respectively.…”

Section: Introduction and Basic Conceptsmentioning

confidence: 99%

Browder spectra of upper-triangular operator matrices

Zhang¹,

Du²

2006

Journal of Mathematical Analysis and Applications

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Let M C = A C 0 B be a 2 × 2 upper triangular operator matrix acting on the Hilbert space H ⊕ K. In this paper, for given operators A and B, we prove thatthe Browder resolvent of an operator T and C∈B(K,H) σ (M C ) has been determined in [H.K. Du, P. Jin, Perturbation of spectrums of 2 × 2 operator matrices, Proc. Amer. Math. Soc. 121 (1994) 761-776]. Moreover, we explore the relations of σ (A) ∪ σ (B) \ σ (M C ), σ b (A) ∪ σ b (B) \ σ b (M C ) and σ w (A) ∪ σ w (B) \ σ w (M C ), where σ (A), σ b (A) and σ w (A) denote the spectrum, the Browder spectrum and the Weyl spectrum of A, respectively.

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Weyl’s theorem for upper triangular operator matrices

Cited by 16 publications

References 9 publications

Generalized Weyl’s theorem and property (gw) for upper triangular operator matrices

Generalized Weyl’s theorem and property (gw) for upper triangular operator matrices

Weyl type theorems of 2×2 upper triangular operator matrices

Browder spectra of upper-triangular operator matrices

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