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Ein Schwach-Stark-Prinzip der Dualitätstheorie lokalkonvexer Räume als Fortsetzungsmethode. (German) Zbl 0389.46026
MSC:
46E40Spaces of vector- and operator-valued functions
46M05Tensor products of topological linear spaces
46A13Spaces defined by inductive or projective limits (LB, LF, etc.)
46A11Spaces determined by compactness or summability properties
46A30Open mapping and closed graph theorems; completeness
46A20Duality theory of topological linear spaces
46A22Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46F05Topological linear spaces of test functions, distributions and ultradistributions
References:
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[2]Bierstedt, K.D., Gramsch, B., Meise, R.: Approximationseigenschaft, Lifting und Kohomologie für lokalkonvexe Produktgarben. Manuscripta math.19, 319-364 (1976) · Zbl 0335.46019 · doi:10.1007/BF01278923
[3]Boland, P.J., Waelbroeck, L.: The nuclearity ofH(U). Preprint 1975
[4]Bungart, L.: Holomorphic functions with values in locally convex spaces and applications to integral formulas. Trans. Amer. math. Soc.111, 317-344 (1964) · Zbl 0142.33902 · doi:10.1090/S0002-9947-1964-0157004-9
[5]De Wilde, M.: Reseaux dans les espaces à semi-normes. Mém. Soc. roy. Sci. Liège, Coll. 8o, V. ser.18, fasc. 2 (1969)
[6]Gramsch, B.: Inversion von Fredholmfunktionen bei stetiger und holomorpher Abhängigkeit von Parametern. Math. Ann.214, 95-147 (1975) · Zbl 0326.47031 · doi:10.1007/BF01352647
[7]Gramsch, B.: Über das Cauchy-Weil-Integral für Gebiete mit beliebigem Rand. Arch. der Math.28, 409-421 (1977) · Zbl 0449.46049 · doi:10.1007/BF01223944
[8]Gramsch, B.: Über eine Fortsetzungsmethode der Dualitätstheorie lokalkonvexer Räume. Ausarbeitung, Kaiserslautern WS 75/76
[9]Grothendieck, A.: Produits tensoriels topologiques et espaces nucléaires. Amer. math. Soc. Mem. 16 (1955)
[10]Grothendieck, A.: Topological vector spaces. New York: Gordon and Breach 1973
[11]Hörmander, L.: Linear partial differential operators. Berlin-Heidelberg-New York: Springer 1963
[12]Horváth, J.: Topological vector spaces and distributions. Reading: Addison Wesley 1966
[13]Horváth, J.: Finite parts of distributions. In: Proceedings of the Conference on Linear Operators and Approximation (Oberwolfach 1971), pp. 142-158. Birkhäuser Basel 1972
[14]Kaballo, W.: Liftingsätze für vektorwertige Funktionen und das ?-Tensorprodukt. Habilitationsschrift, Kaiserslautern 1976
[15]Komatsu, H.: Ultradistributions, I. Structure theorems and a characterization. J. Fac. Sci., Univ. Tokyo, Sect. I A20, 25-105 (1973)
[16]Köthe, G.: Topologische lineare Räume. Berlin-Heidelberg-New York: Springer 1960
[17]Meise, R.: Räume holomorpher Vektorfunktionen mit Wachstumsbedingungen und topologische Tensorprodukte. Math. Ann.199, 293-312 (1972) · Zbl 0241.46036 · doi:10.1007/BF01431482
[18]Nachbin, L.: On vector valued versus scalar valued holomorphic continuation. Indagationes Math.35, 352-354 (1973) · doi:10.1016/1385-7258(73)90032-2
[19]Pietsch, A.: Nukleare Funktionenräume. Math. Nachr.33, 377-384 (1967) · Zbl 0145.38103 · doi:10.1002/mana.19670330511
[20]Schaefer, H.H.: Topological vector spaces. New York: McMillan 1966
[21]Schottenloher, M.: ?-product and continuation of analytic mappings. In: Colóquio de Análise (Rio de Janeiro 1972), pp. 261-270. Paris: Hermann 1975
[22]Tillmann, H.G.: Eine Erweiterung des Funktionalkalküls für lineare Operatoren. Math. Ann.151, 424-430 (1963) · Zbl 0121.33404 · doi:10.1007/BF01439452
[23]Vogt, D.: Tensorprodukte von (F)- mit (DF)-Räumen und ein Fortsetzungssatz. Preprint Wuppertal 1975
[24]Waelbroeck, L.: Weak analytic functions and the closed graph theorem. In: Proceedings on infinite dimensional holomorphy (Kentucky 1973), pp. 97-100. Lecture Notes in Mathematics364. Berlin-Heidelberg-New York: Springer 1974
[25]Gramsch, B., Wagner, R.: Eine Bemerkung zur Division von Distributionen durch analytische Operatorfunktionen. Manuscripta math.21, 25-42 (1977) · Zbl 0355.46022 · doi:10.1007/BF01176899
[26]Aingorn, I.B., Brudovskii, B.S.: The extension and lifting of equicontinuous sets of linear mappings. Sibir. Math. J.12, 678-684 (1971) · Zbl 0235.46007 · doi:10.1007/BF00966505