• A NOTE ON Xd -FRAMES IN BANACH SPACES

Ram Bharat Singh, Mahesh C. Joshi, A. K. Sah*

Abstract


Frames with respect to some sequence space, namely-frames were introduced and studied by Casazza et al [1]. We further study-frames and proved if a Banach space has a -frames then it also has the Parseval and an exact Parseval-frames. A necessary and sufficient condition and also a sufficient condition for the stability of -frame have been given. Also, -Bessel sequences, Xfor a sequence to be -frame has been obtained.


Keywords


-frame, -Bessel sequence, Banach frame, Stability, an exact -frame.

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