A new functional calculus for noncommuting operators
Copyright policy )A new functional calculus for noncommuting operators
In this paper we use the notion of slice monogenic functions \cite{slicecss} to define a new functional calculus for an $n$-tuple $T$ of not necessarily commuting operators. This calculus is different from the one discussed in \cite{jefferies} and it allows the explicit construction of the eigenvalue equation for the $n$-tuple $T$ based on a new notion of spectrum for $T$. Our functional calculus is consistent with the Riesz-Dunford calculus in the case of a single operator.
to appear in Journal of Functional Analysis
Functional calculus for linear operators, noncommuting operators, bepress|Physical Sciences and Mathematics|Mathematics, Slice monogenic functions, Several-variable operator theory (spectral, Fredholm, etc.), Noncommuting operators, spectral theory, functional calculus, Mathematics - Spectral Theory, Algebra, slice monogenic functions, 47A10, 47A60, 30G35, Functions of hypercomplex variables and generalized variables, bepress|Physical Sciences and Mathematics|Mathematics|Algebra, Functional calculus, FOS: Mathematics, Spectral theory, Spectral Theory (math.SP), Analysis
Functional calculus for linear operators, noncommuting operators, bepress|Physical Sciences and Mathematics|Mathematics, Slice monogenic functions, Several-variable operator theory (spectral, Fredholm, etc.), Noncommuting operators, spectral theory, functional calculus, Mathematics - Spectral Theory, Algebra, slice monogenic functions, 47A10, 47A60, 30G35, Functions of hypercomplex variables and generalized variables, bepress|Physical Sciences and Mathematics|Mathematics|Algebra, Functional calculus, FOS: Mathematics, Spectral theory, Spectral Theory (math.SP), Analysis
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