Abstract
In the present paper the following theorem is proved: Let E be a barrelled locally convex space with a Schauder base of type P or P. Then E is normable.
In continuation of the investigations of singer [8] and Retherford [5] we obtain by the above result a characterization of the reflexivity of a locally convex space with a base in terms of the behaviour of its subspaces.
Similar content being viewed by others
Literatur
DUBINSKY, E. and J.R. RETHERFORD: Schauder bases and Köthe sequence spaces. Trans. Amer. Math. Soc. 130 (1968) 265–280
HOLUB, J.R.: Bases of type P and reflexivity of Banach spaces. Proc. Amer. Math. Soc. 25 (1970) 357–362
KÖTHE, G.: Topologische lineare Räume. 2. Aufl. Berlin-Heidelberg-New York: Springer 1966
MARTI, J.T.: Introduction to the theory of bases. Berlin-Heidelberg-New York: Springer 1969
RETHERFORD, J.R.: Bases, basic sequences and reflexivity of linear topologtical spaces. Math. Annalen 164 (1966) 280–285
RETHERFORD, J.R. and C.W. MCARTHUR: Some remarks on bases in linear topological spaces. Math. Annalen 164 (1966) 38–41
SCHAEFER, H.H.: Topological vector spaces. New York: Macmillan 1966
SINGER, I.: Basic sequences and reflexivity of Banach spaces, Studia Math. 21 (1962) 351–369
—: Bases in Banach spaces I. Berlin-Heidelberg-New York: Springer 1970
WEILL, L.J.: Unconditional and shrinking bases in locally convex spaces. Pacific J. Math. 29 (1969) 467–483
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mertins, U. Reflexivitât und Schauder Basen vom Typ p und p in Lokalkonvexen Râumen. Manuscripta Math 5, 147–153 (1971). https://doi.org/10.1007/BF01325024
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01325024