Perturbation Formulas for Traces on $C^*$-algebras

Frank Hansen; Gert K. Pedersen

doi:10.2977/prims/1195164797

JournalsprimsVol. 31, No. 1pp. 169–178

Perturbation Formulas for Traces on $C^{*}$ -algebras

Frank Hansen
University of Copenhagen, Denmark
Gert K. Pedersen
University of Copenhagen, Denmark

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Abstract

We introduce the Frechet differential of operator functions on $C^{*}$ -aIgebras obtained via spectral theory from ordinary differentiate functions. In the finite-dimensional case this differential is expressed in terms of Hadamard products of matrices. A perturbation formula with applications to traces is given.

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Frank Hansen, Gert K. Pedersen, Perturbation Formulas for Traces on $C^{*}$ -algebras. Publ. Res. Inst. Math. Sci. 31 (1995), no. 1, pp. 169–178

DOI 10.2977/PRIMS/1195164797