Geodesic
Quotients of F-spaces
Glasgow mathematical journal, Tome 19 (1978) no. 2, pp. 103-108

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a non-locally convex F-space (complete metric linear space) whose dual X′ separates the points of X. Then it is known that X possesses a closed subspace N which fails to be weakly closed (see [3]), or, equivalently, such that the quotient space X/N does not have a point separating dual. However the question has also been raised by Duren, Romberg and Shields [2] of whether X possesses a proper closed weakly dense (PCWD) subspace N, or, equivalently a closed subspace N such that X/N has trivial dual. In [2], the space Hp (0<p<1) was shown to have a PCWD subspace; later in [9], Shapiro showed that lp (0<p<1) and certain spaces of analytic function have PCWD subspaces. Our first result in this note is that every separable non-locally convex F-space with separating dual has a PCWD subspace. 
Kalton, N. J. Quotients of F-spaces. Glasgow mathematical journal, Tome 19 (1978) no. 2, pp. 103-108. doi: 10.1017/S0017089500003463
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[1] 1.Drewnowski, L., On minimally comparable F-spaces, J. Functional Analysis 26 (1977) 315–332. Google Scholar | DOI

[2] 2.Duren, P. L., Romberg, B. W. and Shields, A. L., Linear functionals on H spaces with (0&lt;p&lt;1), J. Reine Angew. Math. 38 (1969) 32–60. Google Scholar

[3] 3.Kalton, N. J., Basic sequences in F-spaces and their applications, Proc. Edinburgh Math. Soc. (2) 19 (1974) 151–167. Google Scholar | DOI

[4] 4.Kalton, N. J., Compact and strictly singular operator on Orlicz spaces, Israel J. Math., 26 (1977) 126–136. Google Scholar | DOI

[5] 5.Kalton, N. J., Universal spaces and universal bases in metric linear spaces, Studia Math., to appear. Google Scholar

[6] 6.Kalton, N. J., Compact p-convex sets, Quart. J. Math. Oxford Ser. 2 28 (1977) 301–308. Google Scholar | DOI

[7] 7.Kalton, N. J. and Shapiro, J. H., An F-space with trivial dual and non-trivial compact endomorphisms, Israel J. Math. 20 (1975) 282–291. Google Scholar | DOI

[8] 8.Kalton, N. J. and Shapiro, J. H., Bases and basic sequences in F-spaces, Studia Math., 56 (1976) 47–61. Google Scholar | DOI

[9] 9.Shapiro, J. H., Examples of proper closed weakly dense subspace in non-locally convex F-spaces, Israel J. Math. 7 (1969) 369–380. Google Scholar | DOI

[10] 10.Shapiro, J. H., Extension of linear functionals on F-spaces with bases, Duke Math. J. 37 (1970) 639–645. Google Scholar | DOI

[11] 11.Waelbroeck, L., Topological Vector Spaces and Algebras, Lecture Notes in Mathematics No. 230 (Springer-Verlag, 1970). Google Scholar

[12] 12.Williamson, J. H., Compact linear operators in linear topological spaces, J. London Math. Soc. 29 (1954) 149–156. Google Scholar | DOI

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