Abstract
We define the ε-product of a ℒ∞-space by a quotient Banach space. We give conditions under which this ε-product will be monic. Finally, we define the ε c -product of a Schwartz b-space by a quotient Banach space and we give some examples of applications.
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Aqzzouz, B.: Le ε-produit dans la catégorie des quotients bornologiques et applications, Thèse de Doctorat, Bruxelles, Mai 1988.
Bartle, R. G. and Graves, L. M.: Mappings between functions spaces, Trans. Amer. Math. Soc. 72 (1952), 400-413.
Bourgain, J. and Delbaen, F.: A class of special L∞-spaces, Acta Math. 145 (1980), 155-176.
Douglas, R. G.: Banach Algebras Techniques in Operator Theory, Academic Press, New York, 1972.
Frampton, J. and Tromba, A.: On the classification of spaces of Hölder continuous functions, J. Funct. Anal. 10 (1972), 336-345.
Hollstein, R.: Inductive limits and ε-tensor products. J. Reine Angew. Math. 319 (1980), 38-62.
Jarchow, H.: Locally Convex Spaces, B. G. Teubner, Stuttgart, 1981.
Kaballo, W.: Lifting theorems for vector valued functions and the ε-product, in Proc. of the First Poderborn Conference on Functional Analysis 27, 1977, pp. 149-166.
Khenkin, G. M.: Impossibility of a uniform homeomorphism between spaces of Smooth functions of one and of nvariables (n > 2), Math. USSR-Sb. 3 (1967), 551-561.
Lindenstrauss, J. and Tzafriri, L.: Classical Banach Spaces, Lecture Notes in Math. 338, 1973.
Nöel, G.: Produit tensoriel et platitude des q-espaces, Bull. Soc. Math. Belgique 22 (1970), 119-142.
Pelsczynski, A.: Sur certaines propriétés isomorphiques nouvelles des espaces de Banach de fonctions holomorphes A(D) et H ∞, C. R. Acad. Sci. Paris 279 (1974), 9-12.
Schwartz, L.: Les théorèmes de Whitney sur les fonctions différentiables, Séminaire Bourbaki 43 (1951), 1-9.
Waelbroeck, L.: Etude spectrale des algèbres complètes, Mém. Cl. Sc. Acad. Roy. Belgique XXXI(7) (1960).
Waelbroeck, L.: Duality and the injective tensor product, Math. Ann. 163 (1966), 122-126.
Waelbroeck, L.: Topological Vector Spaces and Algebras, Lectures Notes in Math. 230, Springer-Verlag, Berlin, 1971.
Waelbroeck, L.: Quotient Banach Spaces, Banach Center Publ., Warsaw, 1982, 553-562 and 563-571.
Waelbroeck, L.: The category of quotient bornological spaces, in J. A. Barosso (ed.), Aspects of Mathematics and its Applications, Elsevier, 1986, pp. 873-894.
Waelbroeck, L.: Holomorphic functions taking their values in a quotient bornological space, Oper. Theory Adv. Appl. 43 (1990), 323-335.
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Aqzzouz, B. The ε c -Product of a Schwartz b-Space by a Quotient Banach Space and Applications. Applied Categorical Structures 10, 603–616 (2002). https://doi.org/10.1023/A:1020940219541
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DOI: https://doi.org/10.1023/A:1020940219541