Glasnik Matematicki, Vol. 50, No. 2 (2015), 415-427.

ON EXCESSES OF FRAMES

Damir Bakić and Tomislav Berić

Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: dbakic@math.hr
e-mail: tberic@math.hr


Abstract.   We show that any two frames in a separable Hilbert space that are dual to each other have the same excess. Some new relations for the analysis resp. synthesis operators of dual frames are also derived. Then we prove that pseudo-dual frames and, in particular, approximately dual frames have the same excess. We also discuss various results on frames in which excesses of frames play an important role.

2010 Mathematics Subject Classification.   42C15.

Key words and phrases.   Frame, Parseval frame, excess.


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DOI: 10.3336/gm.50.2.10


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