Banach格上正则算子格

The Lattices of Regular Operators on Banach Lattices

本文首先对Ｂａｎａｃｈ格Ｅ给出了条件，使得对任意非Ｄｅｄｅｋｉｎｄσ－完备的Ｂａｎａｃｈ格Ｆ，正则算子空间Ｌ＾ｒ（Ｅ，Ｆ）均是一Ｒｉｅｓｚ空间。其次对Ｂａｎａｃｈ格Ｆ给出了一些刻划，使之每个由Ｌ＾ｐ空间到Ｆ内的连续线性了均是正则的。一些相关结果也得以讨论。

In this paper we first present some conditions on Banach lattice E such that the space Lr(E,F) is a Riesz space even if Banach lattice F is not Dedekind a-complete, then we deduce some characterizations on Banach lattice F such that each continuous operator from a Lp-space into F is regular. Some related results are also provided.