Research On Operator-valued Frames

In this thesis, we study operator-valued frames in Hilbert spaces and Hilbert C*-modules. The main works we do as follows. First, given an operator-valued frame, we give some methods to construct a new operator-valued frame satisfying prescribed conditions. Secondly, we generalized the notion of the operator-valued frames to Hilbert C*-module setting and obtain some basic results about dual frames, frame projections, parametrization, frame decomposition and etc. Finally, we introduce operator-valued fusion frame and obtain Dilation Theorem and other properties. Keywords: Hilbert space, Hilbert C*-module, frame, Bessel sequences, decomposition, construction.