Lack of isomorphic embeddings of symmetric function spaces into operator ideals

Abstract

Let E(0, 1) be a symmetric space on (0, 1) and C F be a symmetric ideal of compact operators on the Hilbert space ℓ 2 associated with a symmetric sequence space F . We give several criteria for E(0, 1) and F so that E(0, 1) does not embed into the ideal C F , extending the result for the case when E(0, 1) = Lp(0, 1) and F = ℓp, 1 ≤ p < ∞, due to Arazy and Lindenstrauss [5].