C*-algebras and numerical linear algebra

Details C*-algebras and numerical linear algebra C*-algebras and numerical linear algebra

1992-11-22

arxiv.org/abs/funct-an/9211002v3

Mathematics

Operator Algebras

24 pages, AMS-TeX 2.1

Scientific paper

We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near points of the essential spectrum of the given operator, and we prove that their averages converge to a measure concentrated precisely on the essential spectrum. In the primary cases of interest, namely the discretized Hamiltonians of one-dimensional quantum systems, this limiting measure is associated with a tracial state on a certain simple C*-algebra. These results have led us to conclude that one must view this kind of numerical analysis in the context of C*-algebras.

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