论文信息 - Some remarks on Radon-Nikodym compact spaces

Some remarks on Radon-Nikodym compact spaces

The class of quasi Radon–Nikodým compact spaces is introduced. We prove that this class is closed under countable products and continuous images. It includes the Radon–Nikodým compact spaces. Adapting Alster’s proof we show that every quasi Radon–Nikodým and Corson compact space is Eberlein. This generalizes earlier results by J. Orihuela, W. Schachermayer, M. Valdivia and C. Stegall. Further the class of almost totally disconnected spaces is defined and it is shown that every quasi Radon–Nikodým space which is almost totally disconnected is actually a Radon–Nikodým compact space embeddable in the space of probability measures on a scattered compact space.

A. D. Arvanitakis

[1] I. Namioka. Radon-Nikodým compact spaces and fragmentability , 1987 .

[2] N. Ribarska. Internal characterization of fragmentable spaces , 1987 .

[3] S. Ditor. On a lemma of Milutin concerning averaging operators in continuous function spaces , 1970 .

[4] J. Lindenstrauss,et al. The Structure of Weakly Compact Sets in Banach Spaces , 1968 .

[5] A. D. Arvanitakis,et al. A characterization of regular averaging operators and its consequences , 2002 .

[6] M. Fabian,et al. Remarks on continuous images of Radon-Nikodým compacta , 1998 .

[7] M. Fabian,et al. Gâteaux differentiability of convex functions and topology : weak asplund spaces , 1997 .

[8] A. Arhangel'skii. General Topology II , 1996 .

[9] W. Schachermayer,et al. Every Radon-Nikodym Corson compact space is Eberlein compact , 1991 .

[10] C. Stegall. More facts about conjugate Banach spaces with the Radon-Nikodym property , 1990 .

[11] O. I. Reynov. On a class of Hausdorff compact and GSG Banach spaces , 1981 .

[12] K. Alster. Some remarks on Eberlein compacts , 1979 .

[13] H. Rosenthal. The heredity problem for weakly compactly generated Banach spaces , 1974 .