A functional calculus for subnormal operators

A new functional calculus for noncommuting operators

In this paper we use the notion of slice monogenic functions [2] 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 [5] 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-Du...

Functional Calculus for Non-Commuting Operators

Hyperinvariant Subspaces for Some Subnormal Operators

In this article we employ a technique originated by Enflo in 1998 and later modified by the authors to study the hyperinvariant subspace problem for subnormal operators. We show that every “normalized” subnormal operator S such that either {(S∗nSn)1/n} does not converge in the SOT to the identity operator or {(SnS∗n)1/n} does not converge in the SOT to zero has a nontrivial hyperinvariant subsp...

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.

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.