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Nukleare Räume

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References

  • Banach, S. “Théorie des opérations linéaires”, Warschau 1932

    Google Scholar 

  • Bourbaki, N. “Topologie générale”, Eléments de mathématique, Paris, Hermann, Livre III

    Google Scholar 

  • Bourbaki, N. “Espaces vectoriels topologiques”,..., Livre V

    Google Scholar 

  • “Sur certains espaces vectoriels topologiques”, Ann. Inst. Fourier 2 (1951), 5–16

    Article  MathSciNet  MATH  Google Scholar 

  • Dieudonné, J. [1] “Recent Developments in the Theory of Locally Convex Vector Spaces” Bull. Amer. Math. Soc. 59 (1953), 495–512

    Article  MathSciNet  MATH  Google Scholar 

  • [2] “Sur les espaces de Montel métrisables”, C. R. Acad. Sci. Paris 238 (1954), 194–195

    MathSciNet  MATH  Google Scholar 

  • [1]— u. Gomes, A. P. “Sur certains espaces vectoriels topologiques”, C. R. Acad. Sci. Paris 230 (1950), 1129–1130

    MathSciNet  MATH  Google Scholar 

  • [1]— u. Schwartz, C. “la Dualité dans les espaces (F) et (LF)”, Ann. Inst. Fourier 1 (1949), 61–101

    Article  MathSciNet  MATH  Google Scholar 

  • Dubinsky, E. [1] “Echelon Spaces of Order ∞”, Proc. AMS 16 (1965), 1178–1183

    MathSciNet  MATH  Google Scholar 

  • Dvoretzky, A. und Rogers, C. A. [1] “Absolute and Unconditional Convergence in Normed Linear Spaces”, Proc. Nat. Acad. Sci. USA 36 (1950), 192–197

    Article  MathSciNet  MATH  Google Scholar 

  • Floret, K. “p-integrale Abbbildungen und ihre Anwendung auf Distributionsräume”, Diplomarbeit, Heidelberg (1967)

    Google Scholar 

  • Floret, K. “Zur Regularität kompakter induktiver Spektren”, ersch. in Arch. f. Math.

    Google Scholar 

  • Gelfand, I.M. u.a. “Verallgemeinerte Funktionen (Distributionen)”, Bd. 1–4, Dtsch. Verl. d. Wiss., Berlin 1960 ff

    Google Scholar 

  • Grothendieck, A. [1] “Espaces vectoriels topologiques,” Publ. Soc. Mat., S. Paulo, 1958

    MATH  Google Scholar 

  • Grothendieck, A. “Produits tensoriels topologiques et espaces nucléaires”, Mem. AMS 16 (1955)

    Google Scholar 

  • “Sur les espaces (F) et (DF)”, Summa Brasil. Math. 3 (1954) 57–123

    MathSciNet  MATH  Google Scholar 

  • [4] “Sur certaines classes de suites dans les espaces de Banach, et le théorème de Dvoretzky-Rogers”, Boletin Soc. Mat. S. Paulo 8 (1956), 81–110

    MathSciNet  Google Scholar 

  • Hahn, M.H. [1] “Über lineare Gleichungen in linearen Räumen”, J. f. reine u. angew. Math. 157 (1927), 214–229

    MATH  Google Scholar 

  • Halmos, P.R. [1] “Measure Theory”, Van Nostrand, New York 1950

    Book  MATH  Google Scholar 

  • [2] “Introduction to Hilbert Space and the Theorem of Spectral Multiplicity”, Chelsea, New York 1957 (2. Aufl.)

    MATH  Google Scholar 

  • Hausdorff, F. [1] “Grundzüge der Mengenlehre”, Chelsea, New York 1949 (Neuauflage des 1914 erschienen Originals)

    MATH  Google Scholar 

  • Hewitt, E. u. Stromberg, K. [1] “Real and Abstract Analysis”, Springer, Berlin-Heidelberg-New York 1965

    Book  MATH  Google Scholar 

  • Husain, T. [1] “The Open Mapping and Closed Graph Theorems in Topolgical Vector Spaces,” Vieweg, Braunschweig 1965

    Book  MATH  Google Scholar 

  • Kantorowitsch, L. W. u. Akilow, G. P. [1] “Funktionalysis in normierten Räumen”, Akad. Verl., Berlin 1964

    MATH  Google Scholar 

  • Kelley, J. L. [1] “General Topology”, Van Nostrand, New York 1955

    MATH  Google Scholar 

  • Kolmogoroff, A. [1] “Zur Normierbarkeit eines topologischen Raumes”, Stud. Math. 5 (1934), 29–34

    MATH  Google Scholar 

  • Komatsu, H. [1] “Projective and Injective Limits of Weakly Compact Sequences of Locally Convex Spaces”, J. Math. Soc. Japan, 19 (1967), 366–383

    Article  MathSciNet  MATH  Google Scholar 

  • Komura, Y. [1] “A Few Problems Concerning Linear Topological Spaces”, Sûgaku 15 (1963/64) 218–221 (jap., Ref: Zbl. 135 (1967), 343)

    MathSciNet  Google Scholar 

  • [2] “Some Examples in Linear Topological Spaces”, Math. Ann. 15 (1964), 150–162

    Article  MathSciNet  MATH  Google Scholar 

  • Köthe, G., [1] “Topologische lineare Räume,” Springer, Berlin-Göttingen-Heidelberg 1966 (2. Aufl.)

    Book  MATH  Google Scholar 

  • [2] “Bericht über neuere Entwicklungen in der Theorie der topologischen Vektorräume”, Jber. DMV 59 (1957) 19–34

    MATH  Google Scholar 

  • “Die Stufenräume, eine einfache Klasse vollkommener Räume”, Math. Zeitschr. 51 (1948), 317–345

    Article  MATH  Google Scholar 

  • [4] “Über die Vollständigkeit einer Klasse lokalkonvexer Räume,”, Math. Zeitschr. 52 (1950), 627–630

    Article  MATH  Google Scholar 

  • Mackey, G. W. [1] “Convex Topological Linear Spaces”, Trans. AMS 60 (1946), 519–537

    Article  MathSciNet  MATH  Google Scholar 

  • Makarov, B. M. [1] “Über induktive Limiten normierter Räume,” Dokl. A.N. 119 (1958), 1092–1094 (russ.)

    Google Scholar 

  • [2] “Über pathologische Eigenschaften induktiver Limiten von Banachräumen” Usp. Mat. Nauk. 18 (1963), 3 171–178 (russ.)

    MATH  Google Scholar 

  • Maurin, K. [1] “Abbildungen vom Hilbert-Schmidtschen Typus und ihre Anwendungen”, Math. Scand. 9 (1961), 359–371

    MathSciNet  MATH  Google Scholar 

  • [2] “Methods of Hilbert Spaces”, Pol. Scient. Publ. Warszawa 1967

    MATH  Google Scholar 

  • Mitjagin, B.S. [1] “Approximative Dimension und Basen in nuklearen Räumen”, Usp. Mat. Nauk, 16 (1961), 63–132 (russ.)

    MathSciNet  Google Scholar 

  • [2] “Die Nuklearität und andere Eigenschaften der Räume vom Typ (S)”, Trudy Mosk. Mat., Ob-va 9 (1960), 317–328 (russ.)

    MathSciNet  Google Scholar 

  • Nachbin, L. [1] “Topological Vector Spaces of Continuous Functions”, Proc. Nat. Acad. Sci. USA 40 (1954), 417–474

    Article  MathSciNet  MATH  Google Scholar 

  • Natanson, I.P. [1] “Theorie der Funktionen einer reellen Veränderlichen”, Akad. Verl., Berlin 1954

    MATH  Google Scholar 

  • Peŀczyński, A. [1] “A Characterization of Hilbert-Schmidt-Operators”, Studia Math. 28 (1967), 355–360.

    MathSciNet  MATH  Google Scholar 

  • Pietsch, A. [1] “Nukleare lokalkonvexe Räume”, Akad. Verl., Berlin 1965

    MATH  Google Scholar 

  • [2] “Absdut summierende Abbildungen in lokalkonvexen Räumen”, Math. Nachr. 27 (1963), 78–103

    Article  MathSciNet  MATH  Google Scholar 

  • “Absolut-p-summierende Abbildungen in normierten Räumen”, Studia Math. 28 (1967), 333–353

    MathSciNet  MATH  Google Scholar 

  • Pták, V. [1] “On Complete Topological Linear Spaces”, Czech. Math. J., 3, 78 (1953), 301–364.

    MathSciNet  MATH  Google Scholar 

  • [2] “Completeness and the Open Mapping Theorem”, Bull. Soc. math. France 86 (1958), 41–74

    MathSciNet  MATH  Google Scholar 

  • “Some Metric Aspects of the Open Mapping and Closed Graph Theorems”, Math. Ann. 163 (1966), 95–104

    Article  MathSciNet  MATH  Google Scholar 

  • Raikow, D.A. [1] “Über zwei Klassen lokalkonvexer Räume, die in den Anwendungen wichtig sind”, Voronež Gos. Univ. Trudy Sem. Funk. Anal., 5 (1958), 22–34 (russ.)

    Google Scholar 

  • [2], “Vollstetige Spektren lokalkonvexer Räume”, Trudy Mosk. Mat. Ob-va, 7 (1958), 413–438 (russ.)

    Google Scholar 

  • “Vollständigkeitskriterien für lokalkonvexe Räume”, Usp. Mat. Nauk, 14 (1959) 1, 223–229

    Google Scholar 

  • Schatten, R. [1] “Norm Ideals of Completely Continuous Operators”, Ergebn. d. Math. u. Grenzgeb. 27, 1960

    Google Scholar 

  • Silva, J.S. e [1] “Su certi classi di spazi localmente convessi importanti per le applicazioni”, Rend. Mat. e delle sue Appl. 14 (1955), 388–410

    MATH  Google Scholar 

  • Weil, A. [1] “1′Intégration dans les groupes topologiques et ses applications”, Publ. Inst. math. Uni. Strasbourg, Hermann, Paris 1953

    Google Scholar 

  • Wloka, J. [1] “Reproduzierende Kerne und nukleare Räume I”, Math. Ann. 163 (1966), 167–188

    Article  MathSciNet  MATH  Google Scholar 

  • ”, Math. Ann. 172 (1967), 79–93

    Article  MathSciNet  MATH  Google Scholar 

  • Wloka, J. “Kerne und p-integrale Abbildungen”, ersch. in Arch. f. Math.

    Google Scholar 

  • Yosida, K. [1] “Functional Analysis”, Springer, Berlin-Göttingen-Heidelberg 1965

    Book  MATH  Google Scholar 

  • Zaanen, A. C. [1] “An Introduction to the Theory of Integration”, North-Holl. Publ. Comp., Amsterdam 1961

    MATH  Google Scholar 

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Floret, K., Wloka, J. (1968). Nukleare Räume. In: Einführung in die Theorie der lokalkonvexen Räume. Lecture Notes in Mathematics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098576

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