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On Some Convexity Properties of Orlicz Sequence Spaces Equipped with the Luxemburg Norm

✍ Scribed by Henryk Hudzik; Diethard Pallaschke

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
876 KB
Volume
186
Category
Article
ISSN
0025-584X

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✦ Synopsis

Rotundity of finite-diii~eilsioiial Orlin spaces 1: equipped with the Luxemburg nomi is considered. It is proved that criteria for rotundity of 1: for 11 2 3 does not depend on 11 and are the same as the criteria for rotundity of the inhite-dimensional subspace h* of an Orlicz sequence ~p a c e . 1 ~. Criteria for rotundity of 1; are different. Next, criteria for exposed points, (H)-points, strongly exposed points and LUR-points of the unit sphere of 1 ' and of its subspace h* are given.

'l'his functional is convex, even and if c E 1 ' and Z*(Xz) = 0 for any X > 0 then e = 0. So, I* is a convex modular (see [21]). Every Orlicz function 0 generates the Orlicz *equence space 1* defined by I" =; { z = ( x i ) E 1' : Z*(AZ) 4 +m for some A > 0) i = l 1991 Maihtmaiics Subjeci Clarsificaiion. Primary 46330; Secondary 46B 20. Keywords and phrarer. Orlicz space, Luxemburg norm, extreme point, exposed point, strongly -xpored point, (H)-point, LUR-point, (H)-property of compact convex acts.

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