Structured Parseval Frames in Hilbert $C^*$-modules

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dc.creatorJing, Wu
dc.creatorHan, Deguang
dc.creatorMohapatra, Ram
dc.date2006-03-03
dc.date.accessioned2026-07-07T07:06:30Z
dc.date.available2026-07-07T07:06:30Z
dc.descriptionWe investigate the structured frames for Hilbert $C^{*}$-modules. In the case that the underlying $C^{*}$-algebra is a commutative $W^*$-algebra, we prove that the set of the Parseval frame generators for a unitary operator group can be parameterized by the set of all the unitary operators in the double commutant of the group. Similar result holds for the set of all the general frame generators where the unitary operators are replaced by invertible and adjointable operators. Consequently, the set of all the Parseval frame generators is path-connected. We also obtain the existence and uniqueness results for the best Parseval multi-frame approximations for multi-frame generators of unitary operator groups on Hilbert $C^*$-modules when the underlying $C^{*}$-algebra is commutative.
dc.descriptionTo appear in AMS Contemp. Math. (GPOTS-2005 Proceeding)
dc.identifierhttps://arxiv.org/abs/math/0603091
dc.identifierhttp://arxiv.org/abs/math/0603091
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110049
dc.subjectFunctional Analysis
dc.subjectOperator Algebras
dc.subject46C05; 47B10
dc.titleStructured Parseval Frames in Hilbert $C^*$-modules
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