Frames in Hilbert C*-modules and C*-algebras - Texas A&M University (TAMU) Scholar

We present a general approach to a module frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the ideas of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert bases, of reconstruction of the frames by projections and by other bounded module operators with suitable ranges. We obtain frame representation and decomposition theorems, as well as similarity and equivalence results. Hilbert space frames and quasi-bases for conditional expectations of finite index on C*-algebras appear as special cases. Using a canonical categorical equivalence of Hilbert C*-modules over commutative C*-algebras and (F)Hilbert bundles, the results are reinterpretated for frames in vector and (F) Hilbert bundles.

Frames in Hilbert C-modules and C-algebras Academic Article