اصغر رحیمی

Let K be a bounded operator. K-frames are ordinary frames for the range K. These frames are a generalization of or- dinary frames and are certainly different from these frames.This research introduces a new concept of bases fortherange K. Here we define the K-orthonormal basis and the K-Riesz basis, and then we describe their properties.As might be expected,the K-bases differ from the ordinary ones mentioned in this article.