This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aron, R., Compact polynomials and compact differentiable mappings between Banach spaces, in "Seminaire Pierre Lelong (Analyse) Année 1974/75", Springer Lectures Notes Math. 524 (1976), p. 213–222.
Aron, R., Schottenloher, M., Compact holomorphic mappings on Banach spaces and the approximation property, J. Functional Analysis 21 (1976), 7–30.
Bierstedt, K.-D., Meise, R., Lokalkonvexe Unterräume in topologischen Vektorräumen und das c-Produkt, manuscripta math. 8 (1973), 143–172.
Blasco, J.L., Two problems on kR-spaces, Acta Math. Sci. Hung. 32 (1978), 27–30.
Gordón Bombal, F., Llavona González J.L., La propriedad de aproximación en espacios de funciones diferenciables, Revista Acad. Ci. Madrid 70 (1976), 727–741.
Colombeau, J.F., Sur les applications differentiables et analytiques au sens de J. Sebastião e Silva, to appear in Port. Math.
Colombeau, J.F., Spaces of C∞-mappings in infinitely many dimensions and applications, preprint Bordeaux 1977.
Colombeau, J.F., Meise, R., Perrot, B., A density result in spaces of Silva holomorphic mappings, Pacific J. Math., 84 (1979), 35–42.
Gramsch, B., Zum Einbettungssatz von Rellich bei Sobolevräumen, Math. Z. 106, 81–87 (1968).
Hogbe-Nlend, H., Bornologies and functional analysis, North-Holland Mathematics Studies 26 (1977).
Horváth, J., Topological vector spaces and distributions I, Reading, Mass., Addison Wesley 1965.
Keller, H.H., Differential calculus in locally convex spaces, Springer Lecture Notes in Math. 417 (1974).
Meise, R., Spaces of differentiable functions and the approximation property, p. 263–307 in "Approximation Theory and Functional Analysis" J.B. Prolla (Editor), North Holland Mathematics Studies (1979).
Meise, R., Nicht-Nuklearität von Räumen beliebig oft differenzierbarer Funktionen, to appear in Arch. Math. (1980).
Nachbin, L., Sur la densité des sous-algèbres polynomiales d'applications continument différentiables, in Seminaire P. Lelong, H. Skoda (Analyse) Année 1976/77, Springer Lect. Math. 694, 196–203.
Nachbin, L., On the closure of modules of continuously differentiable mappings, preprint, to appear in Rendiconti del Seminário Matemático dell'Università di Padova 59 (1979).
Paques, O.W., The approximation property for certain spaces of holomorphic mappings, p. 351–370 in "Approximation Theory and Functional Analysis", J.B. Prolla (Editor), North Holland Mathematics Studies (1979).
Pietsch, A., Nuclear locally convex spaces, Ergebnisse der Math. 66, Springer (1972).
Prolla, J.B., Guerreiro, C.S., An extension of Nachbin's theorem to differentiable functions on Banach spaces with the approximation property, Ark. Mat. 14, 251–258 (1976).
Schaefer, H.H., Topological Vector Spaces, Springer 1970.
Schwartz, L., Théorie des distributions à valeurs vectorielles I, Ann. Inst. Fourier 7, 1–142 (1957).
Sebastião e Silva, J., Le calcul différentiel et intégral dans les espaces localement convexes réels ou complexes, Att. Acad. Naz. Lincei 20, 743–750 (1956) and 21, 40–46 (1956).
Sebastião e Silva, J., Les espaces à bornés et la notion de fonction différentiable, p. 57–61 in "Colloque d'Analyse Fonctionelle CBRM" (1961).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Colombeau, JF., Meise, R. (1981). C∞-functions on locally convex and on bornological vector spaces. In: Machado, S. (eds) Functional Analysis, Holomorphy, and Approximation Theory. Lecture Notes in Mathematics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089275
Download citation
DOI: https://doi.org/10.1007/BFb0089275
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10560-2
Online ISBN: 978-3-540-38529-5
eBook Packages: Springer Book Archive