Dual properties and joint spectra for solvable Lie algebras of operators

Abstract

Given $L$ a solvable Lie Algebra of operators acting on a Banach space $E$, we study the action of the opposite algebra of $L$, $L^{\prime }$, on $E^{\ast }$. Moreover, we extend Słodkowski joint spectra, ${\sigma }_{\delta ,k}$, ${\sigma }_{\pi ,k}$, and we study its usual spectral properties.

10 pages, original research article

Cited by in corpus (4)

• On Cartan Joint Spectra
• Joint spectrum for quasi-solvable Lie algebras of operators
• On the joint spectra of the two dimensional Lie algebra of operators in Hilbert spaces
• Joint spectra and nilpotent Lie algebras of linear transformations