Abstract
We calculate Fréchet derivatives of the mapping \(a\mapsto f(a)\), where a is a member of a complex unital Banach algebra and f is a complex analytic function in a neighborhood of the spectrum of a. Thus, the connection between the Fréchet derivative and the analytic functional calculus is established.
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Sorina Barza.
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Djordjević, D.S. Fréchet Derivative and Analytic Functional Calculus. Bull. Malays. Math. Sci. Soc. 43, 1205–1212 (2020). https://doi.org/10.1007/s40840-019-00736-6
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DOI: https://doi.org/10.1007/s40840-019-00736-6