Musielak-Orlicz序列空间的H性质(英文)

H-property in Musielak - Orlicz sequence spaces

H性质是Banach空间几何理论中的一个重要性质,H点是H性质的精细化、点态化。在经典Orlicz序列空间中,H点和H性质已被讨论过(见[8]).给出了赋Orlicz范数和赋Luxemburg范数的Musielak-Orlicz序列空间中的H点的判别准则,作为推论,得到了Musielak-Orlicz序列空间在两种范数下具有H性质的充分必要条件。

H -property is an important property in the geometry of Banach space and H -point is precise and pointwise property of H -property. In classical Orlicz sequence spaces, H -point and H-property have been investigated (see [8]). Criteria of H -point in Musielak - Orlicz sequence spaces in the case of the Orlicz norm as well as the Luxemburg norm are given. As a corollary, the necessary and sufficient condition that Musielak -Orlicz sequence spaces for both norms have H -property is given.