Geodesic
Extending Edgar's ordering to locally convex spaces
Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 175-188

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

By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively. 
Robertson, Neill. Extending Edgar's ordering to locally convex spaces. Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 175-188. doi: 10.1017/S0017089500008697
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[1] 1.Bourgin, R. D., Geometric aspects of convex sets with the Radon-Nikodým property. Lecture Notes in Mathematics 993 (Springer-Verlag, 1983). Google Scholar | DOI

[2] 2.Buchwalter, H., Espaces localement convex semi-faibles, Ileme Coll. Anal. Fonct.Bordeaux 1973, Pub. Dep. Math. Lyon 10 (1973). Google Scholar

[3] 3.Dierolf, P., Theorems of the Orlicz-Pettis type for locally convex spaces, Manuscripta Math. 20 (1977), 73–94. Google Scholar | DOI

[4] 4.Dierolf, P. and Dierolf, S., Topological properties of the dual pair <ℬ(Ω)′ ℬ(Ω8)″), Pacific J. Math. 108 (1983, 51–82). Google Scholar | DOI

[5] 5.Diestel, J., Sequences and series in Banach spaces, Graduate Texts in Mathematics 92 (Springer-Verlag, 1984). Google Scholar | DOI

[6] 6.Drewnowski, L., Another note on Kalton's theorem, Studia Math. 52 (1975), 233–237. Google Scholar | DOI

[7] 7.Edgar, G. A., Measurability in a Banach space II, Indiana Univ. Math. J. 28 (1979), 559–579. Google Scholar | DOI

[8] 8.Edgar, G. A., An ordering for the Banach spaces, Pacific J. Math. 108 (1983), 83–98. Google Scholar | DOI

[9] 9.Faires, B. T., Varieties and vector measures, Math. Nachr. 85 (1978), 303–314. Google Scholar | DOI

[10] 10.Floret, K., Weakly compact sets, Lecture Notes in Mathematics 801 (Springer-Verlag, 1980). Google Scholar | DOI

[11] 11.Freniche, F. J., Grothendieck locally convex spaces of continuous vector valued functions, Pacific J. Math. 120 (1985), 345–355. Google Scholar | DOI

[12] 12.Freniche, F. J., Some remarks on the average range of a vector measure, Proc. Amer. Math. Soc. 107 (1989), 119–124. Google Scholar | DOI

[13] 13.Garnir, H. G., De Wilde, M. and Schmets, J., Analyse Fonctionelle Tome I, (Birkhäuser-Verlag, 1968). Google Scholar

[14] 14.Geitz, R. F., Geometry and the Pettis integral, Trans. Amer. Math. Soc. (2) 269 (1982), 535–548. Google Scholar | DOI

[15] 15.Godefroy, G. and Talagrand, M., Classes d'espaces de Banach à prédual unique. C.R. Acad. Sci. Paris 292 (1981), 323–325. Google Scholar

[16] 16.Hunter, R. J. and Lloyd, J., Weakly compactly generated locally convex spaces, Math. Proc. Cambr. Philos. Soc. 82 (1977), 85–98. Google Scholar | DOI

[17] 17.Jarchow, H., Locally convex spaces, (Teubner, 1981). Google Scholar | DOI

[18] 18.Kappeler, T., Banach spaces with the condition of Mazur, Math. Z. 191 (1986), 623–631. Google Scholar | DOI

[19] 19.Kalton, N. and Wilansky, A., Tauberian operators on Banach spaces, Proc. Amer. Math.Soc. 57 (1976), 251–255. Google Scholar | DOI

[20] 20.Lindström, M., A characterization of Schwartz spaces, Math. Z. 198 (1988), 423–430. Google Scholar | DOI

[21] 21.Neidinger, R. D., Concepts in the real interpolation of Banach spaces, Functional Analysis: Proceedings of the Seminar at the University of Texas at Austin, 1986–1987 (Odell, E. and Rosenthal, H., eds), 43–53, Lecture Notes in Mathematics 1332 (Springer-Verlag, 1988). Google Scholar | DOI

[22] 22.Pfister, H., Bemerkungen zum Satz über die Separabilität der Fréchet-Montel-Räume, Arch. Math. (Basel) 27 (1976), 86–92. Google Scholar | DOI

[23] 23.Sentilles, F. D. and Wheeler, R. F., Pettis integration via the Stonian transform, Pacific J. Math. 107 (1983), 473–496. Google Scholar | DOI

[24] 24.Talagrand, M., Espaces de Banach faiblement ℌ-analytiques, Ann. Math. 110 (1979), 407–438. Google Scholar | DOI

[25] 25.Wilansky, A., Mazur spaces, Intern. J. Math. Math. Sci. 4 (1981), 39–55. Google Scholar | DOI

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