This is an announcement for the paper "Basic topological and geometric properties of Cesaro--Orlicz spaces" by Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai and Alicja Szymaszkiewicz.

Abstract: Necessary and sufficient conditions under which the Cesaro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesaro--Orlicz spaces $\cfi$ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in $\cfi$ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces $\cfi$ are given.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B20, 46B45, 46E30

Remarks: 16 pages

The source file(s), mat01.cls: 37258 bytes, mathtimy.sty: 20 bytes, pm2563new.tex: 46836 bytes, is(are) stored in gzipped form as 0607730.tar.gz with size 23kb. The corresponding postcript file has gzipped size 55kb.

Submitted from: Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai and Alicja Szymasz

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http://front.math.ucdavis.edu/math.FA/0607730

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http://arXiv.org/abs/math.FA/0607730

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