利用Banach空间一般理论和广义Orlicz范数的特性,对具有一致Kadec-Klee性质的赋广义Orlicz范数的Orlicz空间进行研究,得到了由N-函数生成的赋广义Orlicz范数的Orlicz空间具有一致Kadec-Klee性质的判据,作为其推论给出了该空间接近一致凸的充要条件.
By using general theories of Banach spaces and the peculiarity of the generalized Orlicz norm, the Orlicz spaces endowed with the generalized Orlicz norm and uniform Kadec-Klee property were studied. For the Orlicz spaces generated by a N-function and endowed with the generalized Orlicz norm, criteria of uniform Kadec-Klee property were presented. As its conclusion, both sufficient and necessary conditions are shown to make these spaces be nearly uniform convex.