Fredholm properties of upper triangular matrices of relations

Huang, Junjie; Du, Yanyan; Huo, Ran

doi:10.1007/s43036-023-00263-z

Adv. Oper. Theory

2023

DOI: 10.1007/s43036-023-00263-z

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Fredholm properties of upper triangular matrices of relations

Junjie Huang

Yanyan Du

Ran Huo

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2024

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Cited by 1 publication

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Weyl-Type Theorems of Upper Triangular Relation Matrices

Du,

Huang

2024

Mathematics

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The spectral theory of operator matrices has several applications in elasticity, quantum mechanics, fluid dynamics, and other fields of mathematical physics. The study of operator matrices is more challenging when the involved operators are not single-valued and should be studied in the context of the theory of relations. In this paper, we utilize the connection between linear relations and their induced operators and use space decomposition methods to characterize the distribution of the spectrum for upper triangular relation matrices. We undertake the same for the essential spectrum, Weyl spectrum, and Browder spectrum. Under certain conditions, we obtain a Browder-type theorem and a Weyl-type theorem for such relation matrices.

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Weyl-Type Theorems of Upper Triangular Relation Matrices

Du,

Huang

2024

Mathematics

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Fredholm properties of upper triangular matrices of relations

Cited by 1 publication

References 19 publications

Weyl-Type Theorems of Upper Triangular Relation Matrices

Weyl-Type Theorems of Upper Triangular Relation Matrices

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