Abstract
Given a nuclear b-space N, we show that if Ω is a finite or σ-finite measure space and 1≤p≤∞, then the functors L loc p(Ω,Nε.) and NεL p(Ω,.) are isomorphic on the category of b-spaces of L. Waelbroeck.
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References
Hogbe-Nlend H., Théorie des Bornologies et Applications, Springer-Verlag, Berlin; Heidelberg; New York (1971). (Lecture Notes in Math.; 213).
Waelbroeck L., Topological Vector Spaces and Algebras, Springer-Verlag, Berlin; Heidelberg; New York (1971). (Lecture Notes in Math.; 230).
Waelbroeck L., “Duality and the injective tensor product,” Math. Ann., 163, 122–126 (1966).
Jarchow H., Locally Convex Spaces, B. G. Teubner, Stuttgart (1981).
Lindenstrauss J. and Tzafriri L., Classical Banach Spaces, Springer-Verlag, Berlin (1973). (Lecture Notes in Math.; 338).
Kaballo W., “Lifting theorems for vector valued functions and the ?-product,” in: Proc. of the First Poderborn Conference on Functional Analysis, 1977, 27, pp. 149–166.
Aqzzouz B., “Généralisations du Théorème de Bartle-Graves,” C. R. Acad. Sci. Paris, 333, No. 10, 925–930 (2001).
Houzel C. (ed) Séminaire Banach, Springer-Verlag, Berlin; Heidelberg; New York (1972). (Lecture Note in Math.; 277).
Henkin G. M., “Impossibility of a uniform homeomorphism between spaces of smooth functions of one and of n variables (n ? 2),” Math. USSR-Sb., 3, 551–561 (1967).
Frampton J. and Tromba A., “On the classification of spaces of Hölder continuous functions,” J. Funct. Anal., 10, 336–345 (1972).
Diestel J. and Uhl J., Vector Measures, AMS, Providence (1985). (Math. Surveys, 15).
Bartle R. G. and Graves L. M., “Mappings between function spaces,” Trans. Amer. Math. Soc., 72, 400–413 (1952).