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The criterion for k-smooth points of the Orlicz sequence space endowed with the Orlicz norm is proved. The necessary and sufficient conditions of k-smoothness of l M and l （M ） are obtained, respectively. Finally, we give the counterexamples which show that previous results are not true. 相似文献
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The sufficient and necessary conditions of the Bochner-Orlicz sequence spaces equipped with the Luxemburg norm,which have λ property,are given.The result shows,which is not as usual,that the λ property of the Bochner-Orlicz seauence spaces can not be lift from X. 相似文献
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LetB(X)andS(X)standfortheunitballandunitsphereofanormedspaceX ,respectively .x∈S(X)iscalledanextremepointofB(X) providedthatfory ,z∈B(X) ,x =y z2 implies y =z .DenotethesetofallextremepointsofB(X)byExtB(X) .XiscalledrotundprovidedthatS(X) =ExtB(X) .Therotundspacesarerelatedtotheoperationresearch ,thecontroltheory ,etc[1] . LetΦbeaevenconvexfunctionwithΦ(0 ) =0 ;Φ(u) >0 (u≠ 0 ) ;limu→ ∞ Φ (u) = ∞ .LetXbeanormedspace ,G Rnbeaboundedmeasurableset ,and (G ,∑ ,μ)beameasur… 相似文献
4.
The sufficient and necessary conditions of the Bochner-Orlicz sequence spaces equipped with the Luxemburg norm,which have λ property,are given.The result shows,which is not as usual,that the λ property of the Bochner-Orlicz seauence spaces can not be lift from X. 相似文献
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