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Norm attaining composition operators on Segal-Bargmann spaces

Neeru Bala, Sudip Ranjan Bhuia

Abstract

In this note, we study the composition operators on Segal-Bargmann spaces, which attains its norm and we show that every composition operators on the classical Fock space over $\mathbb{ C}^n$ is norm attaining. Also, we establish a necessary and sufficient condition for a sum of two kernel functions to be an extremal function for the norm of composition operators.

Norm attaining composition operators on Segal-Bargmann spaces

Abstract

In this note, we study the composition operators on Segal-Bargmann spaces, which attains its norm and we show that every composition operators on the classical Fock space over is norm attaining. Also, we establish a necessary and sufficient condition for a sum of two kernel functions to be an extremal function for the norm of composition operators.
Paper Structure (4 sections, 14 theorems, 40 equations)

This paper contains 4 sections, 14 theorems, 40 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Norm attaining composition operators on $\mathcal{H(E)}$
  4. Extremal functions

Key Result

Theorem 2.1

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

Theorems & Definitions (30)

  • Theorem 2.1
  • Proposition 2.2
  • Theorem 2.3
  • Theorem 2.4
  • Theorem 2.5
  • Remark 2.6
  • Theorem 2.7
  • Remark 3.1
  • Proposition 3.2
  • proof
  • ...and 20 more