Hyperinvariant subspaces for bilateral weighted shifts
type: Item
instance of: scholarly article
title: Hyperinvariant subspaces for bilateral weighted shifts
zbMATH Open document ID: 0574.47005
DOI: 10.1007/BF01204909
author: Constantin Apostol
published in: Integral Equations and Operator Theory
publication date: 1984-01-01T00:00:00Z
review text: Let \(H\) be a complex Hilbert space with the orthonormal basis \(\{e_ n\}_{n\in \mathbb{Z}}\) and let \(U\) be an invertible bilateral weighted shift defined by \(Ue_ n = p_ n e_{n+1}\), \(p_ n>0\), \(n\in\mathbb{Z}\). Then \(U\) has a proper hyperinvariant subspace, if the set \([r_-, R_-] \cup [r_+, R_+]\) is not a singleton set included in \(\{r\} \cup \{R\}\), where \[ \begin{alignedat}{2} r_+&=\varliminf_{k\to\infty} (p_0 \ldots p_{k-}) ^{1/k},\quad& R_+&=\varlimsup_{k\to\infty}(p_0 \ldots p_{k-}) ^{1/k},\\ r_-&=\varliminf_{k\to\infty}(p_{-k} \ldots p_-) ^{1/k},\quad& R_-&=\varlimsup_{k\to\infty}(p_{-k} \ldots p_-)^{1/k},\\ r&=| U^{-1}|^{-1}_{sp},\quad& R&=| U|_{sp}. \end{alignedat} \] On the other side the used technique is an analysis of real sequences and has as byproduct a new proof of a related, on this area well known, theorem of Chevreau-Pearcy-Shields.
Mathematics Subject Classification ID: 47A15
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 3917038
zbMATH Keywords: invertible bilateral weighted shift
zbMATH Keywords: proper hyperinvariant subspace
zbMATH Keywords: theorem of Chevreau-Pearcy-Shields
MaRDI profile type: Publication
cites work: Some invariant subspaces for subnormal operators
cites work: Q3039954
cites work: Q3254057
full work available at URL: https://doi.org/10.1007/bf01204909
OpenAlex ID: W1986863376
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description: scientific article; zbMATH DE number 3917038