Modular frames for Hilbert C-modules and symmetric approximation of frames

摘要

We give a comprehensive introduction to a general modular frame construction in Hilbert C~*-modules and to related linear operators on them. The Hilbert space situation appears as a special case. The reported investigageons rely on the idea of geometirc dilation to standard Hilbert C~*-modules over unital C~*-algebras that admit an orthonormal modular Riesz basis. Interrelations and applications to classical frame theory are indicated. Resorting to frames in Hiblert spaces we discuss some measures for pairs of frames to be close to one another. In particluar, the existence and uniqueness of the closest (normalized0 tight frame to a given frame is investigated. For Riesz bases with certain restrictions the set of closest tight frames often contains a multiple of its symmetric orthogonalization.