An alternative polynomial Daugavet property

Elisa R. Santos. "An alternative polynomial Daugavet property." Studia Mathematica 224.3 (2014): 265-276. <http://eudml.org/doc/285672>.

@article{ElisaR2014,
abstract = {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 $max_\{ω∈\} ||Id + ωP|| = 1 + ||P||$. 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.},
author = {Elisa R. Santos},
journal = {Studia Mathematica},
keywords = {polynomial; alternative polynomial Daugavet property; Daugavet property},
language = {eng},
number = {3},
pages = {265-276},
title = {An alternative polynomial Daugavet property},
url = {http://eudml.org/doc/285672},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Elisa R. Santos
TI - An alternative polynomial Daugavet property
JO - Studia Mathematica
PY - 2014
VL - 224
IS - 3
SP - 265
EP - 276
AB - 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 $max_{ω∈} ||Id + ωP|| = 1 + ||P||$. 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.
LA - eng
KW - polynomial; alternative polynomial Daugavet property; Daugavet property
UR - http://eudml.org/doc/285672
ER -