Ｐ型基和良性有界算子

在自反Ｂａｎａｃｈ空间上一个有界线性算子是（Ｂ）型良性有界的当且仅当它的共扼算子也是（Ｂ）型的。但在非自反Ｂａｎａｃｈ空间上这种性质不成立。本文证明在一大类非自反Ｂａｎａｃｈ空间上总存在一个（Ｂ）型良性有界线性算子，它的共扼算子不是（Ｂ）型的。同时也证明了在具有基的Ｂａｎａｃｈ空间上，任何Ｐ型基序列一定有一个子序弄能够扩张成该空间的一个基。

BASIS OF TYPE P AND WELL-BOUNDED OPERATORS

A linear operator on reflexive Banach spaces is well-bounded of type(B)if and only if its adjoint is.In general,this is no longer possessed on nonreflexive Banach spaces.In this paper,we show that on a very large class of nonreflexive Banach spaces,one can always find a well-bounded operator of type (B) whose adjoinl is not of type(B).It is also proved that a basic sequence of type P must have a subsequence which can be extended to be a basis in Banach spaces with a basis.