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A differentiation in locally convex spaces

  • Sadayuki Yamamuro (a1)

Abstract

The theory of F-finite linear operators developed by Robert T. Moore is used to construct a differential calculus in locally convex spaces. This note contains the fundamental theory up to the implicit function theorem.

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References

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[1]Garnir, H.G., Schmets, M. De Wilde et J., Analyse fonationnelle. Théorie oonstruetive des espaces linéaires à semi-normes. I: Théorie générale (Lehrbücher und Monographien aus dem Gebiete der Exakten Wissenschaften. Mathematische Reihe, 36. Birkhäuser Verlag, Basel und Stuttgart, 1968).
[2]Marinescu, G., “Théorèmes des contractions dans les espaces localement convexes”, Rev. Roumaine Math. Pures Appl. 14 (1969), 15351538.
[3]Moore, Robert T., “Banach algebras of operators on locally convex spaces”, Bull. Amer. Math. Soc. 75 (1969), 6873.
[4]Smale, S., “An infinite dimensional version of Sard's theorem”, Amer. J. Math. 87 (1965), 861866.
[5]Yamamuro, Sadayuki, Differential calculus in topological linear spaces (Lecture Notes in Mathematics, 374. Springer-Verlag, Berlin, Heidelberg, New York, 1974.)
[6]Yamamuro, S., “Notes on differential calculus in topologieal linear spaces, II”, J. Austral. Math. Soc. (to appear).
[7]Yamamuro, S., “Notes on differential calculus in topologieal linear spaces, III”, J. Austral. Math. Soc. (to appear).
[8]Yamamuro, S. and Grunau, John, “Notes on differential calculus in topologieal linear spaces”, J. reine angew. Math. (to appear).
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A differentiation in locally convex spaces

  • Sadayuki Yamamuro (a1)

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