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Maps preserving ascent/descent of triple Jordan product

Roja Hosseinzadeh, Tatjana Petek

Abstract

Let $\mathcal{X}$ be a real or complex Banach space with $ \dim \mathcal{X}\geq 3$. We give a complete description of surjective mappings on $\mathcal{B(X)}$ that preserve the ascent of Jordan triple product of operators or, preserve the descent of Jordan triple product of operators.

Maps preserving ascent/descent of triple Jordan product

Abstract

Let be a real or complex Banach space with . We give a complete description of surjective mappings on that preserve the ascent of Jordan triple product of operators or, preserve the descent of Jordan triple product of operators.
Paper Structure (3 sections, 14 theorems, 28 equations)

This paper contains 3 sections, 14 theorems, 28 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Proof of the main result

Key Result

Theorem 1.1

Let $\mathcal{X}$ be at least three-dimensional Banach space over the field $\mathbb{F}$, being either the field of complex or the field of all real numbers. Let $\phi:\mathcal{B(X)} \to \mathcal{B(X)}$ be a surjective map satisfying the condition or, If $\mathcal{X}$ is infinite-dimensional space, then either there exists an invertible bounded linear or conjugate-linear operator $A: \mathcal{X}

Theorems & Definitions (28)

  • Theorem 1.1
  • Remark 1.2
  • Example 1.3
  • Lemma 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • proof
  • Lemma 2.4
  • proof
  • ...and 18 more