Results in Mathematics

, Volume 63, Issue 1, pp 241-250

First online:

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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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


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