The Research Of Some Properties In Musielak-Orlicz Sequence Spaces

As is known to all, Musielak-Orlicz spaces is a class of important Banachspaces, it is the generalization of classic Orlicz spaces. It plays a very important rolein the research of the theory and application of classical Banach spaces. Variousproperties and their criteria of Musielak-Orlicz spaces provide intuitive anddistinctive materials for the study of general Banach spaces. Musielak-Orlicz spacesestablishes a concrete model for the application of the theory of Banach spaces. Themethods and counterexamples are also provided for the research of the theory ofgeneral Banach spaces. Therefore, it is valuable and theoretically significant toinvestigate the geometric properties of Musielak-Orlicz spaces. In this paper,compactly strongly convex property, weakly compactly strongly convex propertyand-point in Musilak-Orlicz sequence spaces is discussed. The dissertation isdivided into three parts:In the first part, the background, purpose and significance of the study of thisdissertation are introduced. The domestic and foreign developments of the theory ofOrlicz spaces and Musielak-Orlicz spaces are specifically introduced and the maincontents of this dissertation are briefly described.In the second part, a criterion for compactly strongly convex property andweakly compactly strongly convex property in Musielak-Orlicz sequence spacesequipped with the Orlicz norm is given. And then, the condition that this kind ofspaces has strongly convex property and weakly strongly convex property isobtained. For the subspacehM of order continuous elements of Musielak-Orliczsequence spaces equipped with the Luxemburg norml M, it is proved thath Mhasproperty S is equivalent to thath Mhas property WS and both of them are equivalentto the condition ofN∈δ₂⁰.In the last part, the necessary and sufficient condition is given that point on theunit sphere of Musielak-Orlicz sequence spaces equipped with the Luxemburg normis a-point. As a corollary, a criterion that these spaces have local property （） ispresented.