Journal of Operator Theory

Volume 63, Issue 1, Winter 2010 pp. 191-216.

Taylor functional calculus for supernilpotent Lie algebra of operators

Authors: Anar Dosi
Author institution: Department of Mathematics, Atilim University, Incek 06836, Ankara, Turkey

Summary: The present work is motivated by J.L. Taylor's program on noncommutative holomorphic functional calculus within the Lie algebra framework. We propose a sheaf $\mathfrak{T}_{\mathfrak{g}}$ of germs of formally-radical functions in elements of a finite dimensional nilpotent Lie algebra $\mathfrak{g}$ and prove the functional calculus theorem for an operator family generating a supernilpotent Lie subalgebra based upon the sheaf $\mathfrak{T}% _{\mathfrak{g}}$. This calculus extends Taylor's holomorphic functional calculus for a mutually commuting operator family.

Keywords: Noncommutative holomorphic functions in elements of a Lie algebra, formally-radical functions, noncommutative parametrized complexes, Taylor spectrum, transversality

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