Frame approximation of pseudo-inverse operators

Let T denote an operator on a Hilbert space (H, [.,.]), and let {f(i)}(i=1)(infinity) be a frame for the orthogonal complement of the kernel NT. We construct a sequence of operators {Phi (n)} of the form Phi (n) (.) = Sigma (n)(i=1) [., g(t)(n)]f(i) which converges to the psuedo-inverse T+ of T in the strong operator topology as n --> infinity. The operators {Phi (n)} can be found using finite-dimensional methods. We also prove an adaptive iterative version of the result. (C) 2001 Academic Press.