Title

Dilation of Dual Frame Pairs in Hilbert C*-Modules

Authors

Authors

D. G. Han; W. Jing; D. Larson; P. T. Li;R. N. Mohapatra

Comments

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Abbreviated Journal Title

Results Math.

Keywords

Frames; Riesz bases; dilation; dual frame pairs; frame vectors; unitary; groups; Hilbert C*-modules; ALGEBRAS; Mathematics, Applied; Mathematics

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.

Journal Title

Results in Mathematics

Volume

63

Issue/Number

1-2

Publication Date

1-1-2013

Document Type

Article

DOI Link

http://dx.doi.org/10.1007/s00025-011-0195-9

Language

English

First Page

241

Last Page

250

WOS Identifier

WOS:000313870000019

ISSN

1422-6383

Recommended Citation

"Dilation of Dual Frame Pairs in Hilbert C*-Modules" (2013). Faculty Bibliography 2010s. 2550.
https://stars.library.ucf.edu/facultybib2010/2550