## Annals of Functional Analysis

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

### Minimal reducing subspaces of an operator-weighted shift

Munmun Hazarika and Pearl S. Gogoi

#### Abstract

We introduce a family $\mathcal{T}$ consisting of invertible matrices with exactly one nonzero entry in each row and each column. The elements of $\mathcal{T}$ 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 $\mathcal{T}$, 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

**Mathematical Reviews number (MathSciNet)**

MR3717175

**Zentralblatt MATH identifier**

06841334

**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