On a functional calculus for unitary operators in Pontryagin spaces

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 Extensions on Dual Spaces

In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absol...

Functional Calculus on BMO and related spaces

Let f be a Borel measurable function of the complex plane to itself. We consider the nonlinear operator Tf defined by Tf [g] = f ◦ g, when g belongs to a certain subspace X of the space BMO(Rn) of functions with bounded mean oscillation on the Euclidean space. In particular, we investigate the case in which X is the whole of BMO, the case in which X is the space VMO of functions with vanishing ...

$G$-Frames for operators in Hilbert spaces

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

Functional Calculus for Non-Commuting Operators