The bessel sequences, riesz bases and frames in hilbert spaces and Hilbert c*-modules

This thesis consist of five chapters. In the introduction development process oftheory of frames in Hilbert spaces and Hilbert C*-modules were summarized.In the second chapter the basic definitions, concepts, theorems and exampleswhich will be useful in the next chapters have been given.In the third chapter some basic results and theorems about Bessel sequences,orthonormal bases and Riesz bases in Hilbert spaces have been given. Further, anactual application of orthonormal bases in Hilbert spaces have been stated.In the fourth chapter a general theory of frames have been presented and theapplication was mentioned in the second chapter were assessed in the light of frames.In the five and final chapter a general theory of frames, Bessel sequences andRiesz bases in Hilbert C*-modules have been given. In these theories, its emphasizedthat Hilbert C*-modules contain some results which are quite different from thetheories of Hilbert spaces.