Asymptotic expansions for trace functionals

We obtain Taylor approximations for functionals $V\mapsto Tr(f(H_0+V))$ defined on the bounded self-adjoint operators, where $H_0$ 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.