Let \((X,{\cal{B}},\mu)\) be a measure space and A be a norm-closed subalgebra of \({\cal{B}}(L^{p}(X,\mu))\) , where p ∈ [1, ∞). Let (G, A, α) be an Lp-operator algebra dynamical system, where G is a countable discrete amenable group. We prove that the full Lp-operator crossed product Fp(G, A, α) is p-nuclear if and only if A is p-nuclear provided the action α of G on A is p-completely isometric. As applications, we prove that Lp-Cuntz algebras and rotation Lp-operator algebras are p-nuclear. Our results solve a problem raised by N. C. Phillips concerning p-nuclearity for Lp-Cuntz algebras.
