数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (2): 469-476.doi: 10.1016/S0252-9602(16)30013-3

• 论文 • 上一篇    下一篇

SOME PROPERTIES OF OPERATOR-VALUED FRAMES

Laura GAVRUTA, Pasc GAVRUTA   

  1. Politehnica University of Timisoara, Department of Mathematics, Victoriei Square no. 2, 300006 Timisoara, Romania
  • 收稿日期:2014-09-10 修回日期:2015-06-06 出版日期:2016-04-25 发布日期:2016-04-25
  • 通讯作者: Pasc GAVRUTA,E-mail:pgavruta@yahoo.com E-mail:pgavruta@yahoo.com
  • 作者简介:Laura GAVRUTA,E-mail:gavruta laura@yahoo.com
  • 基金资助:

    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.

SOME PROPERTIES OF OPERATOR-VALUED FRAMES

Laura GAVRUTA, Pasc GAVRUTA   

  1. 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.

摘要:

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.

关键词: Frames, g-frames

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

中图分类号: 

  • 42C15