The continuity properties of discrete-spectrum families of Fredholm operators

TL;DR

This paper explores the continuity characteristics of discrete-spectrum families of Fredholm operators, connecting recent definitions with classical operator topology concepts to deepen understanding of their structural properties.

Contribution

It establishes a link between newly introduced discrete-spectrum families and classical continuity properties in operator spaces, advancing theoretical understanding.

Findings

Clarifies the relationship between discrete-spectrum families and classical continuity.

Provides new insights into the topological structure of Fredholm operators.

Enhances the theoretical framework for analyzing operator families.

Abstract

This note relates the notion of a discrete-spectrum family of Fredholm operators, recently introduced by N. Ivanov in arXiv:2111.15081, with the classical continuity properties in the space of operators.