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Hyponormal contractions and analytic shifts

Sneha B, Neeru Bala, Jaydeb Sarkar

Abstract

Hyponormal operators are known to be among the most difficult operators to analyze. In this work, we focus on two finite types of hyponormal operators. The first type becomes analytic shifts, while the second type admits analytic models. A basic model for hyponormal operators plays a key role in our analysis.

Hyponormal contractions and analytic shifts

Abstract

Hyponormal operators are known to be among the most difficult operators to analyze. In this work, we focus on two finite types of hyponormal operators. The first type becomes analytic shifts, while the second type admits analytic models. A basic model for hyponormal operators plays a key role in our analysis.
Paper Structure (6 sections, 6 theorems, 238 equations)

This paper contains 6 sections, 6 theorems, 238 equations.

Table of Contents

  1. Introduction
  2. A basic model
  3. Analytic shifts
  4. Finite-isometries
  5. $n$-finite operators
  6. Examples

Key Result

Proposition 2.1

Let $T\in\mathscr{B}(\mathcal{H})$ be a pure hyponormal contraction. Then where $B\in\mathscr{B}(\mathcal{D}_{T})$ is a contraction, $S\in\mathscr{B}(\mathcal{H}\ominus\mathcal{D}_T)$ is a unilateral shift, and $A\in\mathscr{B}(\mathcal{D}_T,\mathcal{H}\ominus\mathcal{D}_T)$ such that

Theorems & Definitions (17)

  • Definition 1.1
  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Theorem 3.1
  • proof
  • Theorem 4.1
  • proof
  • Proposition 5.1
  • ...and 7 more