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Some study of the approximate orthogonality connected with integral orthogonalities

Ranran Wang, Qi Liu, Jinyu Xia, Yongmo Hu

Abstract

In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to preserve mappings of orthogonality. Moreover, we explore the relationship between this new approximate orthogonality and other forms of approximate orthogonality.

Some study of the approximate orthogonality connected with integral orthogonalities

Abstract

In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to preserve mappings of orthogonality. Moreover, we explore the relationship between this new approximate orthogonality and other forms of approximate orthogonality.
Paper Structure (3 sections, 11 theorems, 67 equations)

This paper contains 3 sections, 11 theorems, 67 equations.

Table of Contents

  1. Introduction
  2. Approximate $HH-I$ orthogonality
  3. Approximately $HH-I$ orthogonality preserving mappings

Key Result

Proposition 2.1

Let any $\varepsilon \in[0,1)$, and all $x,y \in X$. Then the relations $\perp_{H H-I}^{\varepsilon}$ and ${ }^{\varepsilon} \perp_{H H-I}$ ane symmetric. Therefore,

Theorems & Definitions (24)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Proposition 2.1
  • proof
  • Proposition 2.2
  • proof
  • Lemma 3.1
  • Theorem 3.1
  • proof
  • ...and 14 more