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 46L08Secondary 42C1546H25

Keywords

FramesRiesz basesdilationdual frame pairsframe vectorsunitary groupsHilbert 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