Approximative Compactness and Full Rotundity in Musielak-Orlicz spaces and Lorentz-Orlicz spaces
Approximative Compactness and Full Rotundity in Musielak-Orlicz spaces and Lorentz-Orlicz spaces
复制标题
DOI：
10.4171/zaa/1283
复制
发表时间：
2006-06
影响因子：
1.2
通讯作者：
H. Hudzik;Wojciech Kowalewski;G. Lewicki
中科院分区：
文献类型：
--
作者：
H. Hudzik;Wojciech Kowalewski;G. Lewicki
证明了Banach空间X的逼近紧性等价于X的自反性与Kadec-Klee性质的结合。这意味着近似紧性与Rolewicz在Studia Math.85（1987），25 - 35中定义的drop性质一致。利用这个一般性结果，我们找到了Musielak-Orlicz函数类和序列空间中的逼近紧性的判别准则，以及Lorentz-Orlicz空间类中逼近紧性的判别准则.本文还给出了Musielak-Orlicz空间的满凸性的判别准则。给出了自反严格凸Köthe函数空间不是近似紧的一个例子，并对Musielak-Orlicz空间的紧面性质作了一些注记.
We prove that approximative compactness of a Banach space X is equivalent to the conjunction of reflexivity and the Kadec-Klee property of X. This means that approximative compactness coincides with the drop property defined by Rolewicz in Studia Math. 85 (1987), 25 – 35. Using this general result we find criteria for approximative compactness in the class of Musielak–Orlicz function and sequence spaces for both (the Luxemburg norm and the Amemiya norm) as well as critria for this property in the class of Lorentz–Orlicz spaces. Criteria for full rotundity of Musielak–Orlicz spaces are also presented in the case of the Luxemburg norm. An example of a reflexive strictly convex Köthe function space which is not approximatively compact and some remark concerning the compact faces property for Musielak–Orlicz spaces are given.