We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism π of a finite-dimensional solvable Lie algebra 𝔤 in terms of quasispectra σ(π). In particular, we prove that the joint spectral radius of a compact subset in a solvable operator Lie subalgebra coincides with the geometric spectral radius with respect to a quasispectrum.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-2,
author = {Anar Dosiev},
title = {Quasispectra of solvable Lie algebra homomorphisms into Banach algebras},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {13-27},
zbl = {1100.47015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-2}
}
Anar Dosiev. Quasispectra of solvable Lie algebra homomorphisms into Banach algebras. Studia Mathematica, Tome 173 (2006) pp. 13-27. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-2/