Operators on Bourgain–Delbaen spaces

摘要

We prove that, whenever we pick real numbers a,b such that 0 < b < a < 1, a + b > 1, and a3 + b3 = 1, then every bounded linear operator from ℓ2 to Xa,b and from Xa,b to ℓ2 must be compact, where Xa,b is the Bourgain–Delbaen space.