Spaceability of the set of continuous injections from BℓpBℓp into ℓpℓp with nowhere continuous inverses

Let p∈(1,∞)p∈(1,∞). We show that, in the Banach space of all bounded continuous mappings from BℓpBℓp (the open unit ball in ℓpℓp) into ℓpℓp, the subset consisting of all injections with nowhere continuous inverses, is isometrically ℓpℓp-spaceable, i.e. it contains an isometric copy of ℓpℓp. The proof uses some ideas of Creswell's example.