  We numerically construct slowly relaxing local operators in a nonintegrable
spin-1/2 chain. Restricting the support of the operator to $M$ consecutive
spins along the chain, we exhaustively search for the operator that minimizes
the Frobenius norm of the commutator with the Hamiltonian. We first show that
the Frobenius norm bounds the time scale of relaxation of the operator at high
temperatures. We find operators with significantly slower relaxation than the
slowest simple "hydrodynamic" mode due to energy diffusion. Then, we examine
some properties of the nontrivial slow operators. Using both exhaustive search
and tensor network techniques, we find similar slowly relaxing operators for a
Floquet spin chain; this system is hydrodynamically "trivial", with no
conservation laws restricting their dynamics. We argue that such slow
relaxation may be a generic feature following from locality and unitarity.
