Operator Frames in Hilbert Spaces

This text on “Operator Frames in Hilbert Spaces” for students and researchers are self-contained and give more and comprehensive coverage of the topics like Frames, K-frames, g-frames and kg-frames. This book is divided in to five chapters. the first chapter contains brief introduction of this book. Chapter 2 Presents basic information of frames, Bessel sequences, Riesz basis, types of frames in Hilbert spaces and frame operator, Chapter 3 contains the definitions of different types of K- frames and examples, frame operators of K-frames, and some results on K-frame operators are established. K-g-frames have a certain advantage compared with g-frames in practical applications. In Chapter 4 presented the definition and examples of K-g frames. Finally, Chapter 5 gives basic concepts of Krein spaces with examples. Definitions of frames and operator frames in Krein spaces with examples.We believe that we have accurately described the analogues of the scope of the basic results in frame theory. Using K-frames and K-g-frames, we have attempted to partially characterize closed range operators. The notions of 2K frames and 2K-g frames have been presented.