Quasispectra of solvable Lie algebra homomorphisms into Banach algebras
Volume 174 / 2006
Studia Mathematica 174 (2006), 13-27
MSC: Primary 47A60; Secondary 47A13, 17B30.
DOI: 10.4064/sm174-1-2
Abstract
We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism $\pi$ of a finite-dimensional solvable Lie algebra $\mathfrak g$ in terms of quasispectra $\sigma(\pi) $. 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.
