Results in Mathematics

, Volume 63, Issue 1, pp 241–250

Dilation of Dual Frame Pairs in Hilbert C*-Modules

  • Deguang Han
  • Wu Jing
  • David Larson
  • Pengtong Li
  • Ram N. Mohapatra
Article

DOI: 10.1007/s00025-011-0195-9

Cite this article as:
Han, D., Jing, W., Larson, D. et al. Results. Math. (2013) 63: 241. doi:10.1007/s00025-011-0195-9

Abstract

We investigate the geometric properties for Hilbert C*-modular frames. We show that any dual frame pair in a Hilbert C*-module is an orthogonal compression of a Riesz basis and its canonical dual for some larger Hilbert C*-module. This generalizes the Hilbert space dual frame pair dilation theory due to Casazza, Han and Larson to dual Hilbert C*-modular frame pairs. Additionally, for any Hilbert C*-modular dual frame pair induced by a group of unitary operators, we show that there is a dilated dual pair which inherits the same group structure.

Mathematics Subject Classification (2010)

Primary 46L08 Secondary 42C15 46H25 

Keywords

Frames Riesz bases dilation dual frame pairs frame vectors unitary groups Hilbert C*-modules 

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Deguang Han
    • 1
  • Wu Jing
    • 2
  • David Larson
    • 3
  • Pengtong Li
    • 4
  • Ram N. Mohapatra
    • 1
  1. 1.Department of MathematicsUniversity of Central FloridaOrlandoUSA
  2. 2.Department of Mathematics and Computer ScienceFayetteville State UniversityFayettevilleUSA
  3. 3.Department of MathematicTexas A&M UniversityCollege StationUSA
  4. 4.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China