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- Title
Polynomial daugavet centers.
- Authors
Santos, Elisa R
- Abstract
A polynomial |$Q: X \rightarrow Y$| is called a polynomial Daugavet center if the equality $$\begin{equation*} \|Q + P \| = \|Q\| + \|P \| \end{equation*}$$ is satisfied for all rank-one polynomials |$P: X \rightarrow Y$|. In this paper, we present geometric characterizations of polynomial Daugavet centers. We show that if |$Q$| is a polynomial Daugavet center, then every weakly compact polynomial |$P$| also satisfies this equation. Finally, we prove that if |$Y$| is a subspace of a Banach space |$E$| and |$Q: X \rightarrow Y$| is a polynomial Daugavet center, then |$E$| can be equivalent renormed in such a way that the norm on |$Y$| is not modified and |$J \circ Q: X \rightarrow E$| is a polynomial Daugavet center. We also present some examples of polynomial Daugavet centers.
- Subjects
POLYNOMIALS; BANACH spaces
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 4, p1237
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haaa029