DOIAbstract
AbstractWe classify up to isomorphism the spaces of compact operators K(E,F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2m⊕[0,α], the topological sum of Cantor cubes 2m and the intervals of ordinal numbers [0,α]. More precisely, we prove that if 2m and ℵγ are not real-valued measurable cardinals and n⩾ℵ0 is not sequential cardinal, then for every ordinals ξ, η, λ and μ with ξ⩾ω1, η⩾ω1, λ=μ<ω or λ,μ∈[ωγ,ωγ+1[, the following statements are equivalent:(a)K(C(2m⊕[0,λ]),C(2n⊕[0,ξ])) and K(C(2m⊕[0,μ]),C(2n⊕[0,η])) are isomorphic.(b)Either C([0,ξ]) is isomorphic to C([0,η]) or C([0,ξ]) is isomorphic to C([0,αp]) and C([0,η]) is isomorphic to C([0,αq]) for some regular cardinal α and finite ordinals p...
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