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Products of two orthogonal projections

Jaydeep Bhattacharjee, Jaydeb Sarkar

Abstract

We study operators that are products of two orthogonal projections. Our results complement some of the classical results of Crimmins and von Neumann. Particular emphasis has been given to projections associated with inner functions defined on the polydisc.

Products of two orthogonal projections

Abstract

We study operators that are products of two orthogonal projections. Our results complement some of the classical results of Crimmins and von Neumann. Particular emphasis has been given to projections associated with inner functions defined on the polydisc.

Paper Structure

This paper contains 7 sections, 21 theorems, 175 equations.

Table of Contents

  1. Introduction
  2. Crimmins' perspective
  3. Nagy-Foias and Langer’s perspective
  4. von Neumann's perspectives
  5. Inner projections
  6. Model projections
  7. Blaschke products

Key Result

Lemma 2.1

Let $T \in \mathcal{B}(\mathcal{H})$. If $T = P X$ for some projection $P \in \mathcal{B}(\mathcal{H})$ and linear operator $X \in \mathcal{B}(\mathcal{H})$, then

Theorems & Definitions (40)

  • Lemma 2.1
  • proof
  • Proposition 2.2
  • proof
  • Corollary 2.3
  • Proposition 2.4
  • proof
  • Corollary 2.5
  • proof
  • Theorem 2.6
  • ...and 30 more