K-b-Frames for Hilbert Spaces and the b-Adjoint Operator

This paper will generalize b-frames, a new concept of frames for Hilbert spaces, by K-b-frames. The idea is to take a sequence from a Banach space and see how it can be a frame for a Hilbert space. Instead of the scalar product, we will use a new product called the b-dual product, which is constructed via a bilinear mapping. We will introduce new results about this product, about b-frames and K-b-frames and we will also give some examples of both b-frames and K-b-frames that have never been given before. We will express the reconstruction formula of the elements of the Hilbert space. We will also study the stability and preservation of both b-frames and K-b-frames and to do so, we will give the equivalent of the adjoint operator according to the b-dual product.

کلیدواژه ها:

b-frames ، K-b-frames ، b-adjoint ، Hilbert space ، sesquilinear form