2022/05/29 by Janko Bračič, Bračič, Janko, Marko Kandić +1
Mathematics · #47A15 #47B07 #47B10 #47L10 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2205.14732
openalex publication_date 2022/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
We prove the existence of a non-trivial hyperinvariant subspace for several sets of polynomially compact operators. The main results of the paper are: (i) a non-trivial norm closed algebra \mathcal A⊆ \mathcal B(\mathscr X) which consists of polynomially compact quasinilpotent operators has a non-trivial hyperinvariant subspace; (ii) if there exists a non-zero compact operator in the norm closure of the algebra generated by an operator band \mathcal S, then \mathcal S has a non-trivial hyperinvariant subspace.