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Power partial isometries

Kritika Babbar, Amit Maji

Abstract

In this paper we obtain a complete characterization of reducing, invariant, and hyperinvariant subspaces for the completely non-unitary component of a power partial isometry. In particular, precise characterization of reducing, invariant, and hyperinvariant subspaces of a truncated shift operator has been achieved.

Power partial isometries

Abstract

In this paper we obtain a complete characterization of reducing, invariant, and hyperinvariant subspaces for the completely non-unitary component of a power partial isometry. In particular, precise characterization of reducing, invariant, and hyperinvariant subspaces of a truncated shift operator has been achieved.

Paper Structure

This paper contains 5 sections, 18 theorems, 127 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Reducing subspaces of a c.n.u. power partial isometry
  4. Invariant subspaces of a c.n.u. power partial isometry
  5. Hyperinvariant subspaces of a c.n.u. power partial isometry

Key Result

Lemma 2.1

Let $T \in \mathcal{B(H)}$. Then the following are equivalent:

Theorems & Definitions (32)

  • Lemma 2.1: cf. burdak
  • Lemma 2.2: cf. halmospowers
  • Theorem 2.3
  • Theorem 2.4: cf. FF-commutant
  • Definition 2.5
  • Theorem 3.1
  • proof
  • Theorem 3.2
  • proof
  • Remark 3.3
  • ...and 22 more