A Reflexivity Theorem for Subspaces of Calkin Algebras

A linear subspace S of an algebra G is called reflexive if a ∈ S whenever a ∈ G and paq = 0 for every pair p, q of indempotents in G such that pSq = {0}. This paper studies properties of a Banach space that ensure that every separable norm closed linear subspace of the corrsponding Calkin algebra is reflexive. The latter holds for the spaces c0 and ℓp, 1 < p < ∞.