Quasispectra of solvable Lie algebra homomorphisms into Banach algebras

Volume 174 / 2006

Anar Dosiev 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.

Authors

  • Anar DosievDepartment of Mathematics
    Atilim University
    Incek 06836
    Ankara, Turkey
    e-mail
    e-mail

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