Preconditioners and Korovkin-type theorems for infinite-dimensional bounded linear operators via completely positive maps (Q2856673)

The classical approximation theorem of Korovkin was generalized in various settings. The present paper deals with non-commutative Korovkin-type theorems using the modes of convergence induced by strong, weak and uniform eigenvalue clustering of matrix sequences with growing order. An approach which was already considered by the third-named author in the finite-dimensional case, in the setting of preconditioning large linear systems with Toeplitz structure [\textit{S. Serra}, Numer. Math. 82, No. 1, 117--142 (1999; Zbl 0930.65024)], is translated here into the infinite-dimensional context of operators acting on separable Hilbert space.