@Article{Silvestri2010,
author = "Silvestri, Benedetto",
title = "Fréchet differential of a power series in Banach algebras",
journal = "Opuscula Math.",
year = "2010",
volume = "30",
number = "2",
pages = "155--177",
doi = "http://dx.doi.org/10.7494/OpMath.2010.30.2.155",
url = "http://dx.doi.org/10.7494/OpMath.2010.30.2.155",
abstract = "We present two new forms in which the Fréchet differential of a power series in a unitary Banach algebra can be expressed in terms of absolutely convergent series involving the commutant \(C(T) : A \mapsto [A,T]\). Then we apply the results to study series of vector-valued functions on domains in Banach spaces and to the analytic functional calculus in a complex Banach space.",
keywords = "Fréchet differentiation in Banach algebras, functional calculus",
issn = "1232-9274"
}