The space (𝑙_{∞}/𝑐₀,𝑤𝑒𝑎𝑘) is not a Radon space

de María, José L.; Rodríguez-Salinas, Baltasar

doi:10.1090/S0002-9939-1991-1045590-8

The space $(l_ \infty /c_ 0,\;\textrm {weak})$ is not a Radon space
HTML articles powered by AMS MathViewer

by José L. de María and Baltasar Rodríguez-Salinas PDF

Proc. Amer. Math. Soc. 112 (1991), 1095-1100 Request permission

Abstract:

Talagrand [10] gives an example of a Banach space with weak topology which is not a Radon space, independently of their weight. This result gives an answer to a question formulated by Schwartz [9]. In this paper, following the papers of Drewnowski and Roberts [1] and Talagrand [10], we prove that the classical space (${l_\infty }/{c_0}$, weak) is not a Radon space.

References

On the primariness of the Banach space

On measures on Banach spaces with the weak topology

On measurable sets of a

-additive measure

Banach spaces which are Radon spaces with the weak topology

G. Koumoullis, On perfect measures, Trans. Amer. Math. Soc. 264 (1981), no. 2, 521–537. MR 603778, DOI 10.1090/S0002-9947-1981-0603778-X
I. E. Leonard and J. H. M. Whitfield, A classical Banach space: $l_{\infty }/c_{0}$, Rocky Mountain J. Math. 13 (1983), no. 3, 531–539. MR 715776, DOI 10.1216/RMJ-1983-13-3-531

Non-separable metric spaces

25

Walter Schachermayer, Eberlein-compacts et espaces de Radon, C. R. Acad. Sci. Paris Sér. A-B 284 (1977), no. 7, A405–A407. MR 440011

Seminaire Maurey-Schwartz

Michel Talagrand, Sur un théorème de L. Schwartz, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 5, A265–A267 (French, with English summary). MR 507479
Russell C. Walker, The Stone-Čech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83, Springer-Verlag, New York-Berlin, 1974. MR 0380698, DOI 10.1007/978-3-642-61935-9