Almost invertible operators

2022/11/14 by Zakariae Aznay, Aznay, Zakariae, Abdelmalek Ouahab +3
Computer Science · Mathematics · #03Exx #47A10 #47Axx #Advanced Algebra and Logic #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2211.07736

openalex publication_date 2022/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a bounded linear operator T is a direct sum of an invertible operator and an operator with at most countable spectrum iff 0\notinacc^ω₁ σ(T), where ω₁ is the smallest uncountable ordinal and acc^ω₁ σ(T) is the ω₁-th Cantor-Bendixson derivative of σ(T).

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