ﻻ يوجد ملخص باللغة العربية
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. Lowdin orthogonalization).
We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, an
Frames on Hilbert C*-modules have been defined for unital C*-algebras by Frank and Larson and operator valued frames on a Hilbert space have been studied in arXiv.0707.3272v1.[math.FA]. Goal of the present paper is to introduce operator valued frames
We show that every infinite-dimensional commutative unital C*-algebra has a Hilbert C*-module admitting no frames. In particular, this shows that Kasparovs stabilization theorem for countably generated Hilbert C*-modules can not be extended to arbitrary Hilbert C*-modules.
The goal of the present paper is a short introduction to a general module frame theory in C*-algebras and Hilbert C*-modules. The reported investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras th
We investigate the orthogonality preserving property for pairs of mappings on inner product $C^*$-modules extending existing results for a single orthogonality-preserving mapping. Guided by the point of view that the $C^*$-valued inner product struct