Article

Results in Mathematics

, Volume 63, Issue 1, pp 241-250

Dilation of Dual Frame Pairs in Hilbert C*-Modules

  • Deguang HanAffiliated withDepartment of Mathematics, University of Central Florida
  • , Wu JingAffiliated withDepartment of Mathematics and Computer Science, Fayetteville State University Email author 
  • , David LarsonAffiliated withDepartment of Mathematic, Texas A&M University
  • , Pengtong LiAffiliated withDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics
  • , Ram N. MohapatraAffiliated withDepartment of Mathematics, University of Central Florida

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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