Banach空间中凸范数的局部各向一致和局部弱紧一致

Banach Spaces that are LURED and LURWC

本文给出了Ｂａｎａｃｈ空间中的两个局部凸性新概念，即局部各向一致凸（ＬＵＲＥＤ）和局部弱紧一致凸（ＬＵＲＷＣ）．并给出了一个Ｂａｎａｃｈ空间是ＬＵＲＥＤ但既不是ＵＲＥＤ也不是ＬＵＲＷＣ的例子；一个Ｂａｎａｃｈ空间是ＬＵＲＷＣ但不是ＵＲＷＣ的例子以及一个Ｂａｎａｃｈ空间是ＬＵＲＷＣ但不是ＬＵＲＷＣ的例子．

This paper introduces two new rotundity in Banach spaces, that areLURED and LURWC. As a main result,this paper gives three examples,namely aBanach space which is LURED but neither URED nor LURWC,a Banach spaaces whichis LURWC but not URWC,and a Banach Space which is LURWC but not UKWC.