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An alternative polynomial Daugavet property

Elisa R. Santos — 2014

Studia Mathematica

We introduce a weaker version of the polynomial Daugavet property: a Banach space X has the alternative polynomial Daugavet property (APDP) if every weakly compact polynomial P: X → X satisfies $m a x_{ω \in} | | I d + ω P | | = 1 + | | P | |$ . We study the stability of the APDP by c₀-, $ℓ_{\infty}$ - and ℓ₁-sums of Banach spaces. As a consequence, we obtain examples of Banach spaces with the APDP, namely $L_{\infty} (μ, X)$ and C(K,X), where X has the APDP.

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