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Article Citation - WoS: 11Citation - Scopus: 10Cohomology of Sheaves of Frechet Algebras and Spectral Theory(Pleiades Publishing inc, 2005) Dosiev, AAWe propose a holomorpbic functional calculus for a noncommutative operator family generating a supernilpotent Lie subalgebra. This calculus extends Taylor's holomorphic functional calculus.Article Citation - WoS: 6Citation - Scopus: 5Quasispectra of Solvable Lie Algebra Homomorphisms Into Banach Algebras(Polish Acad Sciences inst Mathematics, 2006) Dosiev, AnarWe 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.
