J4 ›› 2011, Vol. 46 ›› Issue (4): 98-102.

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Sequences of Xd Bessel for a Banach space

WANG Ya-li, CAO Huai-xin, ZHANG Qiao-wei   

  1. College of Mathematics and Information Sciences, Shaanxi Normal University, Xi′an 710062, Shaanxi, China
  • Received:2010-01-23 Published:2011-04-21


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 (BXdX,‖·‖) is a Banach space when Xd is a BK-space. By defining an operator Tf, an isometric isomorphism from BXdX 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 independent Xd frames and Xd Riesz bases for a Banach space X are the same.

Key words:  Xd Bessel sequence; Xd frame; Xd Riesz basis

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