Some applications of almost analytic extensions to operator bounds in trace ideals - Nichols, R.; Gesztesy, F. (Methods of Functional Analysis and Topology, 2015)
Using the Davies-Helffer-Sjostrand functional calculus based on almost analytic extensions, we address the following problem: Given a self-adjoint operator S in H, and functions f in an appropriate class, for instance, f C_0^∞(R), how to control the norm \|f(S)\|_B(H) in terms of the norm of the resolvent of S, \|(S - z_0 I_H)^-1\|_B(H), for some z_0 CR. We are particularly interested in the case where B(H) is replaced by a trace ideal, B_p(H), p [1,∞).