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Appropriate locally convex domains for differential calculus


Authors: Richard A. Graff and Wolfgang M. Ruess
Journal: Proc. Amer. Math. Soc. 86 (1982), 331-335
MSC: Primary 58C20; Secondary 46G05, 58D15
DOI: https://doi.org/10.1090/S0002-9939-1982-0667300-0
MathSciNet review: 667300
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Abstract: We make use of Grothendieck's notion of quasinormability to produce a comprehensive class of locally convex spaces within which differential calculus may be developed along the same lines as those employed within the class of Banach spaces and which include the previously known examples of such classes. In addition, we show that there exist Fréchet spaces which do not belong to any possible such class.


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  • [1] C. Bessaga and A. Pelczynski, Selected topics in infinite-dimensional topology, Monografie Matematyczne, vol. 58, Polish Scientific Publishers, Warsaw, 1975. MR 0478168 (57:17657)
  • [2] R. A. Graff, Elements of non-linear functional analysis, Mem. Amer. Math. Soc. 206 (1978).
  • [3] A. Grothendieck, Sur les espaces $ (F)$ et $ (DF)$, Summa Brasil. Mat. 3 (1954), 57-122. MR 0075542 (17:765b)
  • [4] J. Horvath, Topological vector spaces and distributions. I, Addison-Wesley, Reading, Mass., 1966. MR 0205028 (34:4863)
  • [5] J. L. Kelley, General topology, Van Nostrand, New York-London-Toronto, 1955. MR 0070144 (16:1136c)
  • [6] G. Köthe, Topological vector spaces. I, Springer-Verlag, Berlin and New York, 1969. MR 0248498 (40:1750)
  • [7] W. M. Ruess, On the locally convex structure of strict topologies, Math. Z. 153 (1977), 179-192. MR 0454608 (56:12857)
  • [8] -, Strict topologies and $ DF$ spaces, Proc. Paderborn Conf. Functional Anal., 1976, North-Holland Math. Studies, vol. 27, North-Holland, Amsterdam, 1977, pp. 105-118. MR 0500061 (58:17771)
  • [9] E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 0210112 (35:1007)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0667300-0
Article copyright: © Copyright 1982 American Mathematical Society

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