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- W2886324571 abstract "Let K and S be compact Hausdorff spaces and X a Banach lattice with λ + ( X ) > 1 , where λ + ( X ) = inf { max { ‖ x − y ‖ , ‖ x + y ‖ } : ‖ x ‖ = 1 , ‖ y ‖ = 1 and x , y > 0 } . We prove that if T is a positive isomorphism from C ( K ) into C ( S , X ) then for some natural number m there exists an upper semicontinuous set-valued mapping ψ from S to K such that ⋃ s ∈ S ψ ( s ) = K , and each set ψ ( s ) has at most m elements. This result is an extension of a Plebanek theorem, the case X = R . We also show that if ‖ T ‖ ‖ T − 1 ‖ < λ + ( X ) , then m can be taken equal to 1. This result is optimal for the classical spaces X = ℓ p , with 1 ≤ p < ∞ ." @default.
- W2886324571 created "2018-08-22" @default.
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- W2886324571 date "2018-11-01" @default.
- W2886324571 modified "2023-09-24" @default.
- W2886324571 title "On positive embeddings of C(K) spaces into C(S,X) lattices" @default.
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- W2886324571 doi "https://doi.org/10.1016/j.jmaa.2018.08.003" @default.
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