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The β- and γ-duality of sequence spaces

Published online by Cambridge University Press:  24 October 2008

D. J. H. Garling
D. J. H. Garling
Affiliation:
St John's College, Cambridge
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Extract

A K-space (E, τ) is a linear space E of sequences with a locally convex topology τ for which the inclusion map: (E, τ) → (ω, product topology) is continuous. In (2) topological properties of K-spaces were determined directly from properties of the space E and the topology τ. It is, however, very natural to consider duality properties of K-spaces and the purpose of this paper is to determine some of these properties.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 963 - 981
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Dunford, N. and Schwartz, J. T.Linear operators, Part I (New York, 1958).Google Scholar
(2)Garling, D. J. H.On topological sequence spaces. Proc. Cambridge Philos. Soc. 63 (1967), 997–1019.CrossRefGoogle Scholar
(3)Grothendieck, A.Espaces vectoriels topologiques, 3rd ed. (Sao Paulo, 1964).Google Scholar
(4)Köthe, G.Topologische lineare Räume, I (Berlin, 1960).CrossRefGoogle Scholar
(5)Köthe, G.Neubegründung der Theorie der vollkommene Räume. Math. Nachr. 4 (1951), 70–80.CrossRefGoogle Scholar
(6)Köthe, G. and Toeplitz, O.Lineare Räume mit unendlich vielen Koordinaten und Ringe unendlichen Matrizen. J. reine angew. Math. 171 (1934), 193–226.Google Scholar
(7)Persson, A.On a class of conditional Köthe function spaces. Math. Ann. 160 (1965), 131–145.Google Scholar
(8)Pietsch, A.Verallgemeinerte vollkommene Folgenräume (Berlin, 1962).Google Scholar
(9)Webb, J. H. Sequential convergence in locally convex spaces (to appear).Google Scholar