A note on formulae for the generalized Drazin inverse of anti-triangular block operator matrices in Banach spaces

Zhang, Daochang; Jin, Yu; Mosić, Dijana

doi:10.1007/s43037-022-00176-8

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The Drazin Inverse Of Anti-triangular Block Matrices1

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2022

2024

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“…Lately, D. Zhang, Y. Yin and D. Mosić [49] generalized the case BCA = 0 from Theorem 3.4, for operator matrix. Actually, these authors derived the formula for N d when BCA 3 = 0, BCABC = 0 and BCA 2 BC = is valid [49, Theorem 3.2].…”

Section: The Drazin Inverse Of Anti-triangular Block Matricesmentioning

confidence: 99%

Additive Properties of the Drazin Inverse for Matrices and Block Representations: A Survey

Višnjić

2022

FU Math Inform

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Section: The Drazin Inverse Of Anti-triangular Block Matricesmentioning

confidence: 99%

Additive Properties of the Drazin Inverse for Matrices and Block Representations: A Survey

Višnjić

2022

FU Math Inform

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Semigroup Generation Theorems of Anti‐Triangular Operator Matrices and Their Application

Liu,

Huang,

et al. 2024

Journal of Mathematics

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This paper deals with the semigroup generation of anti‐triangular operator matrices M with unbounded entries in Hilbert space. Based on the space decomposition, some necessary and sufficient conditions are given for M to generate contraction semigroups. In addition, the anti‐triangular differential system, converted from the damping wave equation, is used to explain our work, and it is proved that the corresponding anti‐triangular operator matrix satisfies the conditions and generates a contraction semigroup.

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A note on formulae for the generalized Drazin inverse of anti-triangular block operator matrices in Banach spaces

Cited by 2 publications

References 43 publications

Additive Properties of the Drazin Inverse for Matrices and Block Representations: A Survey

Additive Properties of the Drazin Inverse for Matrices and Block Representations: A Survey

Semigroup Generation Theorems of Anti‐Triangular Operator Matrices and Their Application

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