Non Commutative Functional Calculus: Bounded Operators

Non commutative functional calculus: bounded operators

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see [4], and the key tools are a new resolvent operator and a new eigenvalue problem. AMS Classification: 47A10, 47A60, 30G35.

Non commutative functional calculus: unbounded operators

In a recent work, [3], we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from [3] can be extended to the unbounded case, and we highlight the crucial differences between the two cases. In particular, we deduce a new eigenvalue equation, suitable for the construction of a functional calculus for operators whose s...

Non-commutative Functional Calculus

We develop a functional calculus for d-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra.

Functional Calculus for Non-Commuting Operators

A Functional Calculus for Pairs of Commuting Polynomially Bounded Operators

A functional calculus valid for the class of absolutely continuous pairs of commuting polynomially bounded operators is defined.