Abstract
Let T denote an operator on a Hilbert space (H,〈·,·〉), and let {fi}∞i=1 be a frame for the orthogonal complement of the kernel NT. We construct a sequence of operators {Φn} of the form Φn(·)=∑ni=1〈·,gni〉fi which converges to the psuedo-inverse 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.
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