Frame Approximation of Pseudo-Inverse Operators

Let T denote an operator on a Hilbert space · · , and let fi ∞i =1 be a frame for the orthogonal complement of the kernel NT . We construct a sequence of operators n of the form n · = n i=1 · gn i fi which converges to the psuedoinverse T† of T in the strong operator topology as n → ∞. The operators n can be found using finite-dimensional methods. We also prove an adaptive iterative version of the result.