Annals of Functional Analysis

Minimal reducing subspaces of an operator-weighted shift

Munmun Hazarika and Pearl S. Gogoi

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Abstract

We introduce a family T consisting of invertible matrices with exactly one nonzero entry in each row and each column. The elements of T are possibly mutually noncommuting, and they need not be normal or self-adjoint. We consider an operator-valued unilateral weighted shift W with a uniformly bounded sequence of weights belonging to T, and we describe its minimal reducing subspaces.

Article information

Source
Ann. Funct. Anal. Volume 8, Number 4 (2017), 531-546.

Dates
Received: 18 August 2016
Accepted: 9 January 2017
First available in Project Euclid: 29 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.afa/1498723220

Digital Object Identifier
doi:10.1215/20088752-2017-0017

Subjects
Primary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Secondary: 47A15: Invariant subspaces [See also 47A46]

Keywords
operator-weighted sequence space reducing subspace operator-weighted shift

Citation

Hazarika, Munmun; Gogoi, Pearl S. Minimal reducing subspaces of an operator-weighted shift. Ann. Funct. Anal. 8 (2017), no. 4, 531--546. doi:10.1215/20088752-2017-0017. https://projecteuclid.org/euclid.afa/1498723220


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