The Characterizations Of G-p-frames In Complex Banach Spaces

With the development of frame theory, many kinds of frames are put forward, such as:g-frames, p-frames, K-g-frames, Banach frames, ect. g-p-frames are new kind of frames that combined with the concepts of g-frames and p-frames. As new frames, g-p-frames are of great importance to many fields, such as: image and signal processing, neural networks,machine learning, etc. In this paper, we study the g-p-frames, g-q-Riesz bases and multipliers of g-p-Bessel sequences in Banach spaces. The main contents:(1) Based on existing references, we study the g-p-frames and g-q-Riesz bases, intro-duce the concept of dual frame of g-p-frames, and get some properties and characterizations of g-p-frames and g-q-Riesz bases; we also introduce the concept of similar operator, study the stability of g-p-frames based on similar operator.(2) Based on the definition of multipliers of g-p-Bessel sequences, we introduce diago-nal operator. Using bounded operator and diagonal operator, we discuss the adjoint operator,compactness, boundedness and continuity of multipliers of g-p-Bessel sequences.