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Fréchet Derivative and Analytic Functional Calculus

  • Dragan S. DjordjevićEmail author
Article
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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.

Keywords

Fréchet derivative Analytic functional calculus 

Mathematics Subject Classification

46G05 4A60 

Notes

References

  1. 1.
    Bonsall, F.F., Duncan, J.: Complete Normed Algebras. Springer, Berlin (1973)CrossRefzbMATHGoogle Scholar
  2. 2.
    Dunford, N., Schwartz, J.T.: Linear Operators, Part I: General Theory. Interscience Publishers, New York (1958)zbMATHGoogle Scholar
  3. 3.
    Flett, T.M.: Differential Analysis. Cambridge University Press, Cambridge (1980)CrossRefzbMATHGoogle Scholar
  4. 4.
    Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Nauka, Moscow (1977). (in Russian)zbMATHGoogle Scholar
  5. 5.
    Stickel, E.: On the Frechet derivative of matrix functions. Linear Algebra Appl. 91, 83–88 (1987)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences and MathematicsUniversity of NišNisSerbia

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