Glasnik Matematicki, Vol. 43, No.2 (2008), 387-395.

A NOTE ON BLOCK SEQUENCES IN HILBERT SPACES

S. K. Kaushik, Ghanshyam Singh and Virender

Department of Mathematics and Statistics, University College of Science, M.L.S. University, Udaipur (Rajasthan), India
e-mail: Ghanshyamsrathore@yahoo.co.in

Department of Mathematics and Statistics, University College of Science, M.L.S. University, Udaipur (Rajasthan), India
e-mail: virender57@yahoo.com

Abstract.   Block sequences with respect to frames in Hilbert spaces have been defined. Examples have been provided to show that a block sequence with respect to a given frame may not even be a Bessel sequence. Also, a necessary and sufficient condition under which a block sequence with respect to a frame is a frame has been given. Further, applications of block sequences to obtain Fusion frames and Fusion frame systems have been given. Finally, a problem has been posed and observed that an affirmative answer to this problem gives an affirmative answer to the Feichtinger Conjecture.

2000 Mathematics Subject Classification.   42C15, 42A38.

Key words and phrases.   Frame, Bessel sequence, block sequence.

DOI: 10.3336/gm.43.2.11

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