Spaces of nuclear and compact operators without a complemented copy of C(ωω)

These results are generalizations of the classical isomorphic classification of spaces C(α), ω≤α<ω1, due to Bessaga and Pełczyński [7], to the setting of the spaces of operators on X⊕C(α) spaces. The generalization (1) covers the case where X is an ℓ1-predual and Y contains no complemented copy of C(ωω). The generalization (2) covers the case Z=ℓp, 1≤p<∞ and W contains no copy of c0.