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The property $(E_A)$ and local spectral theory

Elvis Aponte, Lourival Lima, José Sanabria

Abstract

In this paper, we introduce and study the spectral property $(E_A)$. This property means that the difference between the approximate point spectrum and the upper semi-Fredholm spectrum coincides with the difference between the approximate point spectrum and the upper semi-Weyl spectrum. Together with local spectral theory, we explore the behavior of this property under certain topological conditions and derive characterizations for the operators that verify it. Furthermore, we establish sufficient conditions that guarantee that a bounded linear operator verifies the property $(E_A)$.

The property $(E_A)$ and local spectral theory

Abstract

In this paper, we introduce and study the spectral property . This property means that the difference between the approximate point spectrum and the upper semi-Fredholm spectrum coincides with the difference between the approximate point spectrum and the upper semi-Weyl spectrum. Together with local spectral theory, we explore the behavior of this property under certain topological conditions and derive characterizations for the operators that verify it. Furthermore, we establish sufficient conditions that guarantee that a bounded linear operator verifies the property .
Paper Structure (5 sections, 12 theorems, 9 equations)

This paper contains 5 sections, 12 theorems, 9 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The property $(E_A)$
  4. Sufficient conditions that implies property $(E_A)$.
  5. Conclusions

Key Result

Theorem 3.5

$\mathbb{T} \in \mathbb{L }(\mathbb{X})$ verifies property $(E_A)$, if and only if, $\mathfrak{S}_{uf}(\mathbb{T}) = \mathfrak{S}_{uw}(\mathbb{T})$.

Theorems & Definitions (30)

  • Example 3.1
  • Example 3.2
  • Definition 3.3
  • Example 3.4
  • Theorem 3.5
  • proof
  • Example 3.6
  • Corollary 3.7
  • proof
  • Lemma 3.8
  • ...and 20 more