Approximation of Pseudo-Inverse Operators by g-Frames

article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Let T denote an operator on a Hilbert space H and let {Λj} be a g-frame for the orthogonal complement of the kernel NT. We construct a sequence of operators {φn} of the form φn(.) = ∑n j=1 g n j (.)Λj which converges to the psuedoinverse T † of T in the strong operator topology as n → ∞. The operators {φn} can be found using finite-dimensional methods. We also prove an adaptive iterative version of the result