Drazin spectrum of operator matrices on the Banach space

Zhang, Shifang; Zhong, Huaijie; Jiang, Qiaofen

doi:10.1016/j.laa.2008.06.002

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Cited by 30 publications

(19 citation statements)

References 20 publications

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“…Proof. Expression (2.8) is the main result of [13], [18] and [19]. Corollary 2.9 shows that the filling some holes in σ * (M C ) should occur in acc σ d (A) ∩ acc σ p (B).…”

Section: Resultsmentioning

confidence: 96%

Generalized Drazin invertibility of operator matrices

Cvetković

2017

Linear and Multilinear Algebra

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“…Proof. Expression (2.8) is the main result of [13], [18] and [19]. Corollary 2.9 shows that the filling some holes in σ * (M C ) should occur in acc σ d (A) ∩ acc σ p (B).…”

Section: Resultsmentioning

confidence: 96%

Generalized Drazin invertibility of operator matrices

Cvetković

2017

Linear and Multilinear Algebra

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“…Proof. First, Theorem 2.9 in [31] told us that Similarly, we can prove that λ ∈ S(B) is also impossible. Thus, we have…”

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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“…Hereafter, the symbol

M_{X}

is reserved for the operator matrix with the form as in . In particular, if

C = 0

, then

M_{X}

admits an upper triangular operator matrix form, which has been productively studied by different authors . For the general case, the invertibility of

M_{X}

was considered by Du and Gu and by Takahashi .…”

Section: Introductionmentioning

confidence: 99%

Weylness of 2 × 2 operator matrices

Huang

Chen

2017

Mathematische Nachrichten

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Let  and  be complex separable infinite-dimensional Hilbert spaces. Given the operators ∈ (), ∈ () and ∈ (, ), we define ∶= [ ] whereis an unknown element. In this paper, a necessary and sufficient condition is given for to be a right Weyl (left Weyl, or Weyl) operator for some ∈ (, ). Moreover, some relevant properties and illustrating examples are also given. K E Y W O R D S

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Drazin spectrum of operator matrices on the Banach space

Cited by 30 publications

References 20 publications

Generalized Drazin invertibility of operator matrices

Generalized Drazin invertibility of operator matrices

Browder spectra of upper-triangular operator matrices

Weylness of 2 × 2 operator matrices

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