Multiple operator integrals and higher operator derivatives

Details Multiple operator integrals and higher operator derivatives Multiple operator integrals and higher operator derivatives

2005-05-26

arxiv.org/abs/math/0505555v3

Mathematics

Spectral Theory

24 pages

Scientific paper

In this paper we consider the problem of the existence of higher derivatives of the function $t\mapsto\f(A+tK)$, where $\f$ is a function on the real line, $A$ is a self-adjoint operator, and $K$ is a bounded self-adjoint operator. We improve earlier results by Sten'kin. In order to do this, we give a new approach to multiple operator integrals. This approach improves the earlier approach given by Sten'kin. We also consider a similar problem for unitary operators.

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