Linear response theory and the KMS condition

The response, relaxation and correlation functions are defined for any vector state ε of a von Neumann algebra (mathfrak{M}) , acting on a Hilbert space ?, satisfying the KMS-condition. An operator representation of these functions is given on a particular Hilbert space . With this technique we prove the existence of the static admittance and the relaxation function. Finally we generalize the fluctuation-dissipation theorem and other relations between the above mentionned functions to infinite systems.