On the differentiability of parametrized families of linear operators and the sensitivity of their stationary vectors
In this article, the differentiability of functions of stationary vectors associated to operator-valued functions as well as the differentiability of the operator-valued functions themselves is studied. In particular, it is shown that the derivative of a weakly differentiable parametric family of continuous operators is again a parametric family of continuous operators. This result is then applied to kernel operators. Further, the sensitivity of continuous linear operators and the sensitivity of their stationary vectors is investigated.
scientific article; zbMATH DE number 5848591
scientific article