Quasispectra of solvable Lie algebra homomorphisms into Banach algebras

Anar Dosiev. "Quasispectra of solvable Lie algebra homomorphisms into Banach algebras." Studia Mathematica 174.1 (2006): 13-27. <http://eudml.org/doc/284574>.

@article{AnarDosiev2006,
abstract = {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.},
author = {Anar Dosiev},
journal = {Studia Mathematica},
keywords = {quasispectra; solvable Lie algebra; functional calculus; joint spectral radius},
language = {eng},
number = {1},
pages = {13-27},
title = {Quasispectra of solvable Lie algebra homomorphisms into Banach algebras},
url = {http://eudml.org/doc/284574},
volume = {174},
year = {2006},
}

TY - JOUR
AU - Anar Dosiev
TI - Quasispectra of solvable Lie algebra homomorphisms into Banach algebras
JO - Studia Mathematica
PY - 2006
VL - 174
IS - 1
SP - 13
EP - 27
AB - 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.
LA - eng
KW - quasispectra; solvable Lie algebra; functional calculus; joint spectral radius
UR - http://eudml.org/doc/284574
ER -