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Every nuclear Frechet space is a quotient of a Köthe Schwartz space. (English) Zbl 0437.46004


MSC:

46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A04 Locally convex Fréchet spaces and (DF)-spaces
46M40 Inductive and projective limits in functional analysis
46A45 Sequence spaces (including Köthe sequence spaces)
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References:

[1] M.Alpseymen, Basic sequences in some nuclear Köthe sequence spaces. Thesis, University of Michigan 1978.
[2] H.Apiola, Characterization of subspaces and quotients of nuclearLf(?, ?)-spaces, preprint. · Zbl 0528.46003
[3] C. Bessaga, Some remarks on Dragilev’s theorem. Studia Math.31, 307-318 (1968). · Zbl 0182.45301
[4] M. M. Dragilev, On regular bases in nuclear spaces. Amer. Math. Soc. Transl. (2)93, 61-82 (1970) (Engl. translation of Math. Sb.68 (110), 153-173 (1965). · Zbl 0206.11905
[5] E. Dubinsky, The structure of nuclear Fréchet spaces. Berlin-Heidelberg-New York, LNM 720 (1979). · Zbl 0403.46005
[6] E. Dubinsky andW. Robinson, Quotient spaces of (s) with basis. Studia Math.63, 39-53 (1978). · Zbl 0393.46012
[7] W. Gejler, On extending an lifting continuous linear mappings in topological vector spaces. Studia Math.62, 295-303 (1978). · Zbl 0398.46007
[8] L.Holmström, A study on the structure of nuclear Köthe spaces. Dissertation, Clarkson College of Technology 1980.
[9] G.Köthe, Topological vector spaces I. Berlin-Heidelberg-New York 1969. · Zbl 0179.17001
[10] A. Martineau, Sur une proprieté universelle de l’espace des distributions de M. Schwartz. C. R. Acad. Sci. Paris259, 3162-3164 (1964). · Zbl 0134.31702
[11] A. Pelczynski, Some problems on bases in Banach and Fréchet spaces. Israel J. Math.2, 132-138 (1964). · Zbl 0203.43203 · doi:10.1007/BF02759953
[12] A.Pietsch, Nuclear locally convex spaces. Berlin-Heidelberg-New York 1972. · Zbl 0308.47024
[13] M. S. Ramanujan andB. Rosenberger, On?(?, P)-nuclearity. Comp. Math.34, 2, 113-125 (1977). · Zbl 0347.46001
[14] T.Terzioglu, Die diametrale Dimension von lokalkonvexen Räumen. Collect. Math.20 (1969). · Zbl 0175.41602
[15] D. Vogt, Charakterisierung der Unterräume vons. Math. Z.155, 109-117 (1977). · Zbl 0337.46015 · doi:10.1007/BF01214210
[16] D. Vogt andM. J. Wagner, Charakterisierung der Quotientenräume vons und eine Vermutung von Martineau. Studia Math.67, 3 (1980). · Zbl 0464.46010
[17] D.Vogt and M. J.Wagner, Charakterisierung der Unterräume und Quotientenräume der nuklearen stabilen Potenzreihenräumen von unendlichem Typ. To appear in Studia Math. · Zbl 0402.46008
[18] M. J.Wagner, Unterräume und Quotienten von Potenzreihenräumen. Dissertation. Wuppertal 1977. · Zbl 0456.46007
[19] V. P. Zahariuta, On the isomorphism of cartesian products of locally convex spaces. Studia Math.46, 201-221 (1973). · Zbl 0261.46003
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