Dilation of Dual Frame Pairs in Hilbert C*-Modules
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- Han, D., Jing, W., Larson, D. et al. Results. Math. (2013) 63: 241. doi:10.1007/s00025-011-0195-9
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.