On Bounded Finite Potent Operators on arbitrary Hilbert Spaces

TL;DR

This paper investigates the structure of bounded finite potent operators on Hilbert spaces, providing insights into the invariant subspace problem, properties of adjoints, and trace equivalences for these operators.

Contribution

It offers a detailed analysis of finite potent operators, addresses the invariant subspace problem for these operators, and establishes trace equivalences for Riesz Trace Class operators.

Findings

Provides an answer to the invariant subspace problem for finite potent operators.

Shows Tate's trace coincides with Leray and R. Elliott's trace for these operators.

Characterizes properties of the adjoint operator of finite potent endomorphisms.

Abstract

The aim of this work is to study the structure of bounded finite potent endomorphisms on Hilbert spaces. In particular, for these operators, an answer to the Invariant Subspace Problem is given and the main properties of its adjoint operator are offered. Moreover, for every bounded finite potent endomorphism we show that Tate's trace coincides with the Leray trace and with the trace defined by R. Elliott for Riesz Trace Class operators.