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Citation - WoS: 21
Citation - Scopus: 20
Cartan-Slodkowski Spectra, Splitting Elements and Noncommutative Spectral Mapping Theorems
(Academic Press inc Elsevier Science, 2006) Dosiev, A
In this paper, we prove Slodkowski version of the infinite-dimensional spectral mapping theorem and Cartan-Slodkowski version of the finite-dimensional spectral mapping theorem for nilpotent operator Lie subalgebras with respect to the various noncommutative functional calculi. (C) 2005 Elsevier Inc. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 5
Quasispectra of Solvable Lie Algebra Homomorphisms Into Banach Algebras
(Polish Acad Sciences inst Mathematics, 2006) Dosiev, Anar
We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism pi of a finite-dimensional solvable Lie algebra 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.