Non-commutative functional calculus: Unbounded operators

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: 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

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

Representations of Hermitian Commutative ∗-algebras by Unbounded Operators

We give a spectral theorem for unital representions of Hermitian commutative unital ∗-algebras by possibly unbounded operators in a pre-Hilbert space. A more general result is known for the case in which the ∗-algebra is countably generated. 1. Statement of the Main Result Our main result is the following: Theorem 1. Let π be a unital representation of a Hermitian commutative unital ∗-algebra A...