Banach格上正则算子

The regular operaters on Banach lattices

首先给出Banach格E上的代数对偶E#,算子对偶E*和序对偶E′之间关系,证明了当E是Banach格时,E*=E′;讨论了典型映射与序对偶之间的关系,证明了当T是正则算子时,‖JT‖r=‖T′‖r;当E是序完备的Banach格,T∈Lr(E)保不相交;P(T)是单射时,T∈Z(E).

Let E be Banach lattice, E~# be its algebra dual,E~*, E′ be the operator dual and order dual, respectively. We show that E~*=E′ when E is a Banach Lattice. The relation between evaluation map and order dual is given. That is, given T∈L^r(E,F), ‖JT‖r=‖T′‖_r; given E as Banach lattice, T∈L^r(E) is has the disjoint preserving and when P(T) is injective, T∈Z(E).