Dilation of Dual Frame Pairs in Hilbert C*-Modules

    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

    Language

    English

    First Page

    241

    Last Page

    250

    WOS Identifier

    WOS:000313870000019

    ISSN

    1422-6383

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