The index of triangular operator matrices

Förster, K.-H.; Nagy, B.

doi:10.1090/S0002-9939-99-05341-1

The index of triangular operator matrices
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by K.-H. Förster and B. Nagy PDF

Proc. Amer. Math. Soc. 128 (2000), 1167-1176 Request permission

Abstract:

For any triangular operator matrix acting in a direct sum of complex Banach spaces, the order of a pole of the resolvent (i.e. the index) is determined as a function of the coefficients in the Laurent series for all the (resolvents of the) operators on the diagonal and of the operators below the diagonal. This result is then applied to the case of certain nonnegative operators in Banach lattices. We show how simply these results imply the Rothblum Index Theorem (1975) for nonnegative matrices. Finally, examples for calculating the index are presented.

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