Abstract: | In this paper, conditions are considered for the existence of the double operator integral ∫∫ ϕ(λ,μ)dEλTdFμ, where Eλ, Fμ are the spectral functions of tow self-adjoint operators A, B on a Hilbert space and T is a bounded operator. In principal,
the case where A has finite spectrum is studied. Nonlinear estimates of ‖f(A)T-T f(B)‖ in terms of the norm of ‖AT-TB‖ for
f∈ Lip 1 are deduced. Also, a formula for the Fréchet derivative is presented. Bibliography: 16 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 148–173.
Translated by S. V. Kislyakov. |