The Daugavet equation for polynomials

• Autorzy: Yun Sung Choi , Domingo García , Manuel Maestre , Miguel Martín
• Języki publikacji: EN

Abstrakty

EN

We study when the Daugavet equation is satisfied for weakly compact polynomials on a Banach space X, i.e. when the equality
||Id + P|| = 1 + ||P||
is satisfied for all weakly compact polynomials P: X → X. We show that this is the case when X = C(K), the real or complex space of continuous functions on a compact space K without isolated points. We also study the alternative Daugavet equation
$max_{|ω|=1} ||Id + ωP|| = 1 + ||P||$
for polynomials P: X → X. We show that this equation holds for every polynomial on the complex space X = C(K) (K arbitrary) with values in X. This result is not true in the real case. Finally, we study the Daugavet and the alternative Daugavet equations for k-homogeneous polynomials.

Kategorie tematyczne

• 46G25: (Spaces of) multilinear mappings, polynomials
• 46B20: Geometry and structure of normed linear spaces
• 47A12: Numerical range, numerical radius

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 178
• Numer: 1
• Strony: 63-84

Daty

wydano

2007

Twórcy

autor

Yun Sung Choi

• Department of Mathematics, POSTECH, Pohang 790-784, Korea

autor

Domingo García

• Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain

autor

Manuel Maestre

• Departamento de Análisis Matemático, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot (Valencia), Spain

autor

Miguel Martín

• Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Identyfikatory

DOI

10.4064/sm178-1-4