GENERALIZED p-FRAME IN SEPARABLE COMPLEX BANACH SPACES

Abstract

The concept of g-frame and g-Riesz basis in a complex Hilbert space was introduced by Sun. 18 In this paper, we generalize the g-frame and g-Riesz basis in a complex Hilbert space to a complex Banach space. Using operators theory and methods of functional analysis, we give some characterizations of a g-frame or a g-Riesz basis in a complex Banach space. We also give a result about the stability of g-frame in a complex Banach space.

Generalized p-fusion frame in separable Banach space

“…Definition 2.6. [2,11] Let { Λ i ∈ B ( X, X i ) : i ∈ I } be a generalized p-frame or g-p-frame for X. Then the operator defined by…”

“…M. R. Abdollahpour et al [2] introduced the p g-frames in Banach spaces. The generalization of the g-frame and g-Riesz Basis in a complex Hilbert space to a complex Banach space was also studied by Xiang-Chun Xio et al [11].…”

Some properties of g-p-frames in complex Banach spaces

“…They were reintroduced and developed in 2003 by Chrisrensen and Stoeva [5]. After several years, Xiao et al [10] generalized the g-frame and g-Riesz basis in a complex Hilbert space to a complex Banach space and obtained some basic properties. From papers [1-3, 5, 6, 8-10], it is known that some properties of g-p-frame are similar to those of p-frame, but the others are not.…”