Banach格上正则AM-紧算子的AM-空间

AM-space and AL-space of Positive AM-compact Operators on Banach Lattices

给出Banach格上所有从E到F的正则AM-紧算子空间在||·||AM范数下是AL-空间,当且仅当E是AM-空间,且F是AL-空间;正则AM-紧算子空间在||·||AM范数下是AM-空间,当且仅当E是AL-空间,F是AM-空间。

It is shown that the space generated by all positive AM-compact operators from E into F,is an AL-space under the ｜｜·｜｜AM-norm if and only if E is an AM-space and F is an AL-space;the space of all positive AM-compact operators from E into F is an AM-space under ｜｜·｜｜AM-norm if and only if E is an AL-space and F is an AM-space.