Abstract
Let Aij i, j=1, 2,..., be operators on a Hilbert spaceX, such that the compound operatorA ∞=A ij ∞i, j=1 induces a bounded positive operator onl 2(X). We show that S(A ∞, theshorted operator (orgeneralized Schur complement), of A∞ can be obtained as the limits of shorts of the operators An, where An is the truncated version ofA ∞, thenA n=A ij ni, j=1 . We use these results to study the short-circuit approximations to infinite networks.
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Morley, T.D. Shorts of block operators and infinite networks—A note on the shorted operator: II. Circuits Systems and Signal Process 9, 161–170 (1990). https://doi.org/10.1007/BF01236449
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DOI: https://doi.org/10.1007/BF01236449