包含广义亚自反空间的Banach空间

Banach spaces containmg the generalized quasi-reflexive Banach subspaces

无穷维Banach空间理论中一个基本问题是:每一个Banach空间都包含一个子空间与c_0或l^1自反空间同构? M·valsivia[1]建立了如下结果。

In this paper we mtroduce the following definition. A mfinitelydimensional Banach space X is called the generalized quasi-reflexive space if there existsanonnegative integer n such that is quasi-reflexive, where X_0=X, X_kJ_k: X→X~? is the canonical imbedding map Moreoverit is calld (m.n)-quasi-reflexive If there exist nonnegativeintegers m and n such that dimX_?=m, dim X_(n-1)≥+∞(n≥1). Our main result gives a class og Banach spaces con-taining this Kind of Banach subspaces.