Symmetric operads in abstract symmetric spectra

We show that all colored symmetric operads in symmetric spectra valued in a symmetric monoidal model category are admissible, i.e., algebras over such operads carry a model structure. For example, this applies to commutative ring spectra and E-infinity-ring spectra in simplicial sets or motivic spaces. Moreover, any weak equivalence of operads in spectra gives rise to a Quillen equivalence of their categories of algebras. For example, any E-infinity-ring spectrum of simplicial sets or motivic spaces can be strictified to a commutative ring spectrum. We apply this to construct a strictly commutative ring spectrum representing Deligne cohomology. We also discuss applications to To\"en-Vezzosi homotopical algebraic contexts and Goerss-Hopkins obstruction theory.