J4 ›› 2011, Vol. 46 ›› Issue (4): 98-102.
• Articles •
WANG Ya-li, CAO Huai-xin, ZHANG Qiao-wei
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.
Xd Bessel sequence; Xd frame; Xd Riesz basis
WANG Ya-li, CAO Huai-xin, ZHANG Qiao-wei. Sequences of Xd Bessel for a Banach space[J].J4, 2011, 46(4): 98-102.
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