A-B-imprimitivity bimodule frames

Abstract

Frames in Hilbert bimodules are a special case of frames in Hilbert C*-modules. The paper considers A-frames and B-frames and their relationship in a Hilbert A-B-imprimitivity bimodule. Also, it is given that every frame in Hilbert spaces or Hilbert C*-modules is a semi-tight frame. A relation between A-frames and K(H_B)-frames is obtained in a Hilbert A-B-imprimitivity bimodule. Moreover, the last part of the paper investigates dual of an A-frame and a B-frame and presents a common property for all duals of a frame in a Hilbert A-B-imprimitivity bimodule.