Banach空间中X_d-Bessel列的性质

The properties of X_d-Bessel sequences in a Banach space

利用算子论方法并结合代数思想,讨论了Banach空间中Xd-Bessel列的一系列性质.证明了当Xd为BK空间时,(BXd(X),.)是数域F上的赋范线性空间;当Xd为CB空间时,(BXd(X),.)是数域F上的Banach空间.通过定义算子Tf,并引入SCB空间的概念,建立了空间BXd(X)和B(X,Xd)之间的等距同构.最后,讨论了λ-BK空间与CB空间的关系,证明了RCB空间必为SCB空间.

A series of properties of Xd-Bessel sequences in a Banach space are discussed by the operator theory and algebraic method.It is proved that（BXd（X）,·） is a normed linear space when Xd is a BK-space and（BXd（X）,·） is a Banach space when Xd is a CB-space.By defining an operator Tf and proposing the definition of SCB-space,an isometric isomorphism from BXd（X） to B（X,Xd） is established,The relations of λ-BK space and CB-space is discussed,and the fact that a RCB-space is also a SCB-space is proved.