Mathematics – Operator Algebras
Scientific paper
2000-10-12
Proceedings of SPIE 4119(2000), 325-336
Mathematics
Operator Algebras
SPIE's Annual Meeting, Session 4119: Wavelets in Signal and Image Processing; San Diego, CA, U.S.A., July 30 - August 4, 2000.
Scientific paper
We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modulesover unital C*-algebras that admit an orthonormal Riesz basis. Interrelations and applications to classical linear frame theory are indicated. As an application we describe the nature of families of operators {S_i} such that SUM_i S*_iS_i=id_H, where H is a Hilbert space. Resorting to frames in Hilbert spaces we discuss some measures for pairs of frames to be close to one another. Most of the measures are expressed in terms of norm-distances of different kinds of frame operators. In particular, the existence and uniqueness of the closest (normalized) tight frame to a given frame is investigated. For Riesz bases with certain restrictions the set of closetst tight frames often contains a multiple of its symmetric orthogonalization (i.e. L\"owdin orthogonalization).
Frank Michael
Larson David R.
No associations
LandOfFree
Modular frames for Hilbert C*-modules and symmetric approximation of frames does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Modular frames for Hilbert C*-modules and symmetric approximation of frames, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Modular frames for Hilbert C*-modules and symmetric approximation of frames will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-84002