English

Finite Operator-Valued Frames

Functional Analysis 2010-09-28 v1

Abstract

Operator-valued frames are natural generalization of frames that have been used in quantum computing, packets encoding, etc. In this paper, we focus on developing the theory about operator-valued frames for finite Hilbert spaces. Some results concerning dilation, alternate dual, and existence of operator-valued frames are given. Then we characterize the optimal operator-valued frames under the case which one packet of data is lost in transmission. At last we construct the operator-valued frames {Vj}j=1m\{V_j\}_{j=1}^m with given frame operator SS and satisfying VjVj=αjIV_jV_j^*=\alpha_jI, where αjs\alpha_j's are positive numbers.

Keywords

Cite

@article{arxiv.1009.5275,
  title  = {Finite Operator-Valued Frames},
  author = {Bin Meng},
  journal= {arXiv preprint arXiv:1009.5275},
  year   = {2010}
}
R2 v1 2026-06-21T16:19:35.877Z