SOME PROPERTIES OF OPERATOR-VALUED FRAMES

doi:10.1016/S0252-9602(16)30013-3

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (2): 469-476.doi: 10.1016/S0252-9602(16)30013-3

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SOME PROPERTIES OF OPERATOR-VALUED FRAMES

Laura GAVRUTA, Pasc GAVRUTA

Politehnica University of Timisoara, Department of Mathematics, Victoriei Square no. 2, 300006 Timisoara, Romania

Received:2014-09-10 Revised:2015-06-06 Online:2016-04-25 Published:2016-04-25
Contact: Pasc GAVRUTA,E-mail:pgavruta@yahoo.com E-mail:pgavruta@yahoo.com
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.

Abstract

Abstract:

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.

Key words: Frames, g-frames

CLC Number:

42C15

Laura GAVRUTA, Pasc GAVRUTA. SOME PROPERTIES OF OPERATOR-VALUED FRAMES[J].Acta mathematica scientia,Series B, 2016, 36(2): 469-476.

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SOME PROPERTIES OF OPERATOR-VALUED FRAMES

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