Quasi-Nilpotent Operators on Locally Convex Spaces

TL;DR

This paper extends the concept of quasi-nilpotent equivalence from Banach spaces to bounded operators on sequentially complete locally convex spaces, broadening the theoretical framework for operator analysis.

Contribution

It introduces the notion of quasi-nilpotent equivalent operators in the setting of locally convex spaces, generalizing prior Banach space results.

Findings

Defines quasi-nilpotent equivalence in locally convex spaces

Establishes properties and implications of these operators

Provides a foundation for further operator theory in locally convex spaces

Abstract

In this article we extend the notion of quasi-nilpotent equivalent operators, introduced by Colojoara and Foias \cite{co1} for Banach spaces, to the class of bounded operators on sequentially complete locally convex spaces.