Acta mathematica scientia, Series B >
SOME PROPERTIES OF OPERATOR-VALUED FRAMES
Received date: 2014-09-10
Revised date: 2015-06-06
Online published: 2016-04-25
Supported by
The final work of P. Gavruta on this article was supported by a grant of Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-JRP-2011-2/11-RO-FR/01.03.2013.
Operator-valued frames (or g-frames) are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this article, we give a new formula for operator-valued frames for finite dimensional Hilbert spaces. As an application, we derive in a simple manner a recent result of A. Najati concerning the approximation of g-frames by Parseval ones. We obtain also some results concerning the best approximation of operator-valued frames by its alternate duals, with optimal estimates.
Laura GAVRUTA , Pasc GAVRUTA . SOME PROPERTIES OF OPERATOR-VALUED FRAMES[J]. Acta mathematica scientia, Series B, 2016 , 36(2) : 469 -476 . DOI: 10.1016/S0252-9602(16)30013-3
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