Asymptotic expansions for trace functionals

We obtain Taylor approximations for functionals V↦Tr(f(H0+V))V↦Tr(f(H0+V)) defined on the bounded self-adjoint operators, where H0H0 is a self-adjoint operator with compact resolvent and f is a sufficiently nice scalar function, relaxing assumptions on the operators made in [17], and derive estimates and representations for the remainders of these approximations.