Analytic operator Lipschitz functions in the disk and a trace formula for functions of contractions

作者：Malamud M M^*; Neidhardt H; Peller V V

来源：Functional Analysis and Its Applications, 2017, 51(3): 185-203.

DOI：10.1007/s10688-017-0183-2

• contraction
• dissipative operator
• trace formulae
• spectral shift function
• operator Lipschitz functions
• perturbation determinant

In this paper we prove that for an arbitrary pair {T (1), T (0)} of contractions on Hilbert space with trace class difference, there exists a function xi in L (1)(T) (called a spectral shift function for the pair {T (1), T (0)}) such that the trace formula trace(f(T (1)) - f(T (0))) = integral(T) f'(zeta)xi(zeta)d zeta holds for an arbitrary operator Lipschitz function f analytic in the unit disk.

• 出版日期2017-7