Explosiveness of Musielak-Orlicz Sequence Spaces

Abstract

In this talk,we make a survey for criteria of the exposed points and the exposedness for the sequence spaces of Orlicz type,such as the classical Orlicz spaces,general Orlicz spaces and Musielak-Orlicz spaces,endowed with Luxemburg norm and Orlicz norm respectively.It is well known that explosiveness is basic concept in the geometric theory of Banach spaces.They have numerous application in separation theory and control theory.Criteria for exposed points and strongly exposed points in all classical Orlicz spaces were given in[10-12].In recent years,Zhao and Cui in[6]discussed the problem in Musielak-Orlicz sequence spaces under some restriction. By counterexamples,we show that the criteria of extreme points in[8]and exposed points in[6] are not true,and we give the criteria for exposed points and strongly exposed points in arbitrary Musielak-Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm by getting rid of the restriction on Musielak-Orlicz function in[6].