On the spectral set of a solvable Lie algebra of operators

TL;DR

This paper investigates the spectral set of a complex solvable Lie algebra of operators on a Banach space, exploring the relationship between the algebra's spectral set and the spectra of its basis elements.

Contribution

It provides new insights into the spectral properties of solvable Lie algebras of operators and their relation to individual basis elements' spectra.

Findings

Established a connection between the spectral set of the algebra and basis element spectra.

Extended spectral analysis to solvable Lie algebras acting on Banach spaces.

Abstract

Given $L$ a complex solvable finite dimensional Lie Algebra of operators acting on a Banach space $E$ and $\{ x_i\}_{1\le i\le n}$ a Jordan-H\"older basis of $ L$, we study the relation between $Sp(L,E)$ and $\Pi Sp(x_i)$.