Opuscula Math. 30, no. 2 (2010), 155-177
http://dx.doi.org/10.7494/OpMath.2010.30.2.155
Opuscula Mathematica
Fréchet differential of a power series in Banach algebras
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.
Mathematics Subject Classification: 58C20, 46H, 47A60.
- Benedetto Silvestri
- Dipartimento di Matematica, Pura ed Applicata via Trieste, 63, 35121 Padova, Italy
- Received: 2009-11-03.
- Revised: 2010-01-08.
- Accepted: 2010-01-10.
