Open AccessFréchet differential of a power series in Banach algebras
Author(s) -
Benedetto Silvestri
Publication year - 2010
Publication title -
opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2010.30.2.155
Subject(s) - mathematics , banach space , banach manifold , power series , banach algebra , unitary state , formal power series , series (stratigraphy) , infinite dimensional vector function , pure mathematics , fréchet derivative , c0 semigroup , convergent series , centralizer and normalizer , interpolation space , lp space , functional analysis , mathematical analysis , paleontology , biology , biochemistry , chemistry , political science , law , gene
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
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