Fréchet Derivative and Analytic Functional Calculus
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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.
KeywordsFréchet derivative Analytic functional calculus
Mathematics Subject Classification46G05 4A60