Remarks on continuous images of Radon-Nikodým compacta
نویسندگان
چکیده
A family of compact spaces containing continuous images of Radon-Nikodým compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikodým compact K we prove: If K is totally disconnected, then it is Radon-Nikodým compact. If K is adequate, then it is even Eberlein compact.
منابع مشابه
Linearly Ordered Radon-nikodým Compact Spaces
We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...
متن کاملConvergent Martingales of Operators and the Radon Nikodým Property in Banach Spaces
We extend Troitsky’s ideas on measure-free martingales on Banach lattices to martingales of operators acting between a Banach lattice and a Banach space. We prove that each norm bounded martingale of cone absolutely summing (c.a.s.) operators (also known as 1-concave operators), from a Banach lattice E to a Banach space Y , can be generated by a single c.a.s. operator. As a consequence, we obta...
متن کاملOn Properties of Compacta That Do Not Reflect in Small Continuous Images
Assuming that there is a stationary set in ω2 of ordinals of countable cofinality that does not reflect, we prove that there exists a compact space which is not Corson compact and whose all continuous images of weight ≤ ω1 are Eberlein compacta. We also prove that under Martin’s axiom countable functional tightness does not reflect in small continuous images of compacta.
متن کاملOn metric characterizations of the Radon-Nikodým and related properties of Banach spaces
We find a class of metric structures which do not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property. Our proof relies on Chatterji’s (1968) martingale characterization of the RNP and does not use the Cheeger’s (1999) metric differentiation theory. The class includes the infinite diamond and both Laakso (2000) spaces. We also show that for each of these structures t...
متن کاملSeparable Zero-dimensional Spaces Which Are Continuous Images of Ordered Compacta
A structure theorem is proved about separable zero-dimensional spaces which are continuous images of ordered compacta and it is shown that not all spaces in this class are orderable themselves.
متن کامل