Operator Differentiable Functions

  • Gert K. Pedersen

    University of Copenhagen, Denmark


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