This is an announcement for the paper "Fragmentability and representations of flows" by Michael Megrelishvili.
Abstract: Our aim is to study weak star continuous representations of semigroup actions into the duals of ``good'' (e.g., reflexive and Asplund) Banach spaces. This approach leads to flow analogs of Eberlein and Radon-Nikodym compacta and a new class of functions (Asplund functions) which intimately is connected with Asplund representations and includes the class of weakly almost periodic functions. We show that a flow is weakly almost periodic iff it admits sufficiently many reflexive representations. One of the main technical tools in this paper is the concept of fragmentability (which actually comes from Namioka and Phelps) and widespreadly used in topological aspects of Banach space theory. We explore fragmentability as ``a generalized equicontinuity'' of flows. This unified approach allows us to obtain several dynamical applications. We generalize and strengthen some results of Akin-Auslander-Berg, Shtern, Veech-Troallic-Auslander and Hansel-Troallic. We establish that frequently, for linear G-actions, weak and strong topologies coincide on, not necessarily closed, G-minimal subsets. For instance such actions are ``orbitwise Kadec``.
Archive classification: Functional Analysis; General Topology
Mathematics Subject Classification: 54H15; 43A60
Citation: Topology Proceedings, 27:2, 2003, 497-544
Remarks: 30 pages
The source file(s), RN.tex: 154972 bytes, diagrams.tex: 116119 bytes, is(are) stored in gzipped form as 0411112.tar.gz with size 82kb. The corresponding postcript file has gzipped size 129kb.
Submitted from: megereli@math.biu.ac.il
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