具有lp-树性质Banach空间的连续嵌入

Continuous embedding of Banach spaces with the l_(p)-tree property

如果Banach空间X中的任意标准弱零树都有一根枝条与l_(p)的标准单位基等价,则X具有l_(p)-树性质.本文证明如果可分自反空间X具有l_(p)(1<p<∞)-树性质,则存在X中一列有限维子空间(X_(i))使得(ΣX_(i))l_(p)的某个稠密子空间连续线性嵌入到X,并且像集在X中稠密.

A Banach space X is said to have thel_(p)-tree property if every normalized weakly null tree in X has a branch that is equivalent to the unit vector basis ofl_(p).In this paper,we prove that if a separable re exive Banach space X has thel_(p)(1<p<∞)-tree property,then there exists a sequence of nite-dimensional subspaces(X_(i))of X so that a dense subspace of(ΣX_(i))l_(p) linearly and continuously embeds into X.Moreover,the image of the embedding is also dense in X.