Intermediate topologies in F-spaces. (English) Zbl 0634.46001
For a non-locally convex F-space (X,\(\tau)\), the author considers the problem of finding intermediate topologies between \(\tau\) and the Mackey topology m(\(\tau)\), giving solutions in various situations.
Reviewer: M.A.Canela
MSC:
| 46A04 | Locally convex Fréchet spaces and (DF)-spaces |
| 46A20 | Duality theory for topological vector spaces |
References:
| [1] | N. J. Kalton, Basic sequences inF-spaces and their applications. Proc. Edinburgh Math. Soc.19, 151-167 (1974). · Zbl 0296.46010 · doi:10.1017/S0013091500010282 |
| [2] | N. J. Kalton andJ. H. Shapiro, Basis and basic sequences inF-spaces. Studia Math.61, 47-61 (1976). · Zbl 0334.46008 |
| [3] | G.Köthe, Topologische lineare Räume I. Grundlehren Math. Wiss.107, Berlin 1960. |
| [4] | A. Nakamura, On the relation between the compatible linear topologies and their bases inF-spaces. Proc. Fac. Sci. Tokai Univ.17, 29-40 (1982). · Zbl 0504.46004 |
| [5] | M. Ribe, Necessary convexity conditions for the Hahn-Banach theorem in metrizable spaces. Pacific J. Math.44, 715-732 (1973). · Zbl 0258.46004 |
| [6] | J. H. Shapiro, Extension of linear functionals onF-spaces with bases. Duke Math. J.37, 639-645 (1970). · Zbl 0205.41002 · doi:10.1215/S0012-7094-70-03779-8 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
