On X ̃-frames and conjugate systems in Banach spaces

Abstract

The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an X~-frame and a system conjugate to X~-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of X~-frame having a conjugate system is studied.

Keywords

• p-frames
• X ̃-frames
• Conjugate systems to X ̃