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The Daugavet equation for polynomials

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Choi Y., García D., Maestre M., Martín M.

Studia Mathematica

2007

tom 178

nr 1

63-84

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.

Ograniczanie wyników

1 Studia Mathematica

1 Choi Y.

1 García D.

1 Maestre M.

1 Martín M.

1 2007

Wyniki wyszukiwania

The Daugavet equation for polynomials