Frechet differential of a power series in a Banach algebra

Details Frechet differential of a power series in a Banach algebra Frechet differential of a power series in a Banach algebra

2008-04-17

arxiv.org/abs/0804.2836v2

Opuscula Math. 30/2 (2010), 155-177

Mathematics

Functional Analysis

24 pages

Scientific paper

We present two new forms in which the Frechet differential of a power series
in a 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 the
analytic functional calculus in a complex Banach space.

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