Closed linear operators between nonarchimedean Banach spaces

Henrı́quez, Hernán R.; Navarro, Horacio; Aguayo, G Jose

doi:10.1016/s0019-3577(05)80023-0

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2024

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Cited by 2 publications

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“…Proposition 2.21. [6] If A ∈ B(E, F ) is surjective, then the induced bijection A 1 : E/N (A) → F is an isomorphism of topological vector spaces.…”

Section: Preliminariesmentioning

confidence: 99%

Common properties of the operator equations in ultrametric specrtal theory

Ettayb

2024

GJOM

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Let X and Y be two ultrametric Banach spaces over K. Let A,D ∈ B(X,Y) and B,C ∈ B(Y,X) such that ABA=ACA (resp. ACD=DBD and DBA=ACA). In this paper, the operator equation ABA=ACA is studied, and the common operator properties of AC-IY and BA-IX are described. In particular, it is proved that N(IY-AC) is complemented in Y if and only if N(IX-BA) is complemented in X. Moreover, the approach is generalized (i.e., CD=DBD and DBA=ACA) for considering relationships between the properties IY-AC and IX-BD. Finally, several illustrative examples are provided.

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“…Proposition 2.21. [6] If A ∈ B(E, F ) is surjective, then the induced bijection A 1 : E/N (A) → F is an isomorphism of topological vector spaces.…”

Section: Preliminariesmentioning

confidence: 99%

Common properties of the operator equations in ultrametric specrtal theory

Ettayb

2024

GJOM

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Ultrametric Fredholm operators and approximate pseudospectrum

Ettayb

2024

AJMS

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PurposeThe paper deals with ultrametric bounded Fredholm operators and approximate pseudospectra of closed and densely defined (resp. bounded) linear operators on ultrametric Banach spaces.Design/methodology/approachThe author used the notions of ultrametric bounded Fredholm operators and approximate pseudospectra of operators.FindingsThe author established some results on ultrametric bounded Fredholm operators and approximate pseudospectra of closed and densely defined (resp. bounded) linear operators on ultrametric Banach spaces.Originality/valueThe results of the present manuscript are original.

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Closed linear operators between nonarchimedean Banach spaces

Cited by 2 publications

References 3 publications

Common properties of the operator equations in ultrametric specrtal theory

Common properties of the operator equations in ultrametric specrtal theory

Ultrametric Fredholm operators and approximate pseudospectrum

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