An alternative polynomial Daugavet property

• Autorzy: Elisa R. Santos
• Języki publikacji: EN

Abstrakty

EN

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
$max_{ω∈𝕋} ||Id + ωP|| = 1 + ||P||$.
We study the stability of the APDP by c₀-, $ℓ_{∞}$- and ℓ₁-sums of Banach spaces. As a consequence, we obtain examples of Banach spaces with the APDP, namely $L_{∞}(μ,X)$ and C(K,X), where X has the APDP.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46G25: (Spaces of) multilinear mappings, polynomials
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 224
• Numer: 3
• Strony: 265-276

Daty

wydano

2014

Twórcy

autor

Elisa R. Santos

• Faculdade de Matemática, Universidade Federal de Uberlândia, Av. João Naves de Ávila 2121, Uberlândia, MG, 38408-100, Brazil

Identyfikatory

DOI

10.4064/sm224-3-4