TY  - JOUR
ID  - Silvestri2010
LB  - Silvestri2010
AU  - Silvestri, Benedetto
TI  - Fréchet differential of a power series in Banach algebras
ST  - Fréchet differential of a power series in Banach algebras
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 2
SP  - 155
EP  - 177
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.2.155
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.2.155
AB  - 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.
KW  - Fréchet differentiation in Banach algebras
KW  - functional calculus
SN  - 1232-9274
ER  -