Banach空间中的X_d Bessel列

Sequences of X_d Bessel for a Banach space

研究了Banach空间X中的Xd Bessel列、Xd框架、Xd独立框架、Xd紧框架与Xd Riesz基。证明了当Xd为BK-空间时,(BXXd,‖·‖)是数域F上的Banach空间;当Xd是BK-空间且X自反时,通过定义算子Tf,建立了空间BXXd与算子空间B(X*,Xd)之间的等距同构,为利用算子论的方法研究Xd Bessel列提供了必要的理论依据。最后,给出了Banach空间X中Xd Bessel列的等价刻画并证明了独立的Xd框架与Xd Riesz基是一致的。

Xd Bessel sequences, Xd frames, Xd independent frames, Xd tight frames and Xd Riesz basis for a Banach space X are introduced and discussed. It is proved that （BXXd,‖·‖） is a Banach space when Xd is a BK-space. By de- fining an operator TI, an isometric isomorphism from Bxxd to B（X＊,Xd ） is established when Xd is a BK-space and X is reflexive, which provides a necessary theoretical basis for studying Xd Bessel sequences by the operator theory. Finally, the equivalent characterizations of Xd Bessel sequences for a Banach space X are given. Also, it is proved that independ- ent Xd frames and Xd Riesz bases for a Banach space X are the same.