On existence of hyperinvariant subspaces for quasinilpotent operators with a nonsymmetry in the growth of the resolvent

2024/04/05 by Maria F. Gamal', Gamal', Maria F.
Mathematics · #47A10 #47A15 #47B01 #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.04348

openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be a quasinilpotent operator on a Banach space. Under assumptions of a certain nonsymmetry in the growth of the resolvent of T, it is proved that every operator in the commutant of T is not unicellular. In particular, T has nontrivial hyperinvariant subspaces. The proof is based on a modification of the reasoning of [S].

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