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arXiv · 0804.2836

Frechet differential of a power series in a Banach algebra

Benedetto Silvestri
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Abstract

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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Benedetto Silvestri. 2012-02-02. Frechet differential of a power series in a Banach algebra. https://arxiv.org/abs/0804.2836

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