Operator Differentiable Functions
Gert K. Pedersen
University of Copenhagen, Denmark
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Abstract
We study the Banach -algebra of -functions on the compact interval such that the corresponding Hilbert space operator function , for and , is Fréchet differentiable. If , we know that the differential is given by the formula
where . Functions of this type are dense in , and , so several classical results can be deduced. In particular we show that if , where is the generator of a one-parameter group of -automorphisms of a -algebra (or just a closed -derivation in ), then for every in , where , and
Cite this article
Gert K. Pedersen, Operator Differentiable Functions. Publ. Res. Inst. Math. Sci. 36 (2000), no. 1, pp. 139–157
DOI 10.2977/PRIMS/1195143229