We study non reflexive Orlicz spaces \(L^\varPsi \) and their Morse subspace \(M^\varPsi \), i.e. the closure of \(L^\infty \) in \(M^\varPsi \) to determine when \((M^\varPsi ,L^\varPsi )\) can be described as having an o–O type structure with respect to an equivalent norm on \(L^\varPsi \). Examples of classes of Young functions for which the answer is affirmative are provided, but also examples are given to show that this is not possible for all non-reflexive Orlicz spaces. An equivalent expression of the distance in \(L^\varPsi \) to \(M^\varPsi \), induced by the new norm, is also provided.

中文翻译：

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具有ao – O型结构的Orlicz空间

我们研究非自反Orlicz空间\（L ^ \ varPsi \）和他们的莫尔斯子空间\（M ^ \ varPsi \）中，即关闭\（L ^ \ infty \）在\（M ^ \ varPsi \） ，以确定当\（（M ^ \ varPsi，L ^ \ varPsi）\）可以描述为相对于\（L ^ \ varPsi \）上的等价范式具有o – O型结构。提供了肯定答案的Young函数类的示例，但同时给出了一些示例，以表明并非所有非自反Orlicz空间都可行。\（L ^ \ varPsi \）到\（M ^ \ varPsi \）的距离的等效表达式还提供了由新规范引入的。