pg-frame in Banach spaces - Rahimi, A.; Faroughi, M. H.; Abdollahpour, M. R. (Methods of Functional Analysis and Topology, 2007)
For extending the concepts of p-frame, frame for Banach spaces and atomic decomposition, we will define the concept of pg-frame and g-frame for Banach spaces, by which each fX (X is a Banach space) can be represented by an unconditionally convergent series f=g_iΛ_i, where {Λ_i}_iJ is a pg-frame, {g_i}(Y_i^*)_l_q and 1p+1q=1. In fact, a pg-frame {Λ_i} is a kind of an overcomplete basis for X^*. We also show that every separable Banach space X has a g-Banach frame with bounds equal to 1.