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The Daugavet equation for polynomials

100%

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.

Integral holomorphic functions

100%

Dimant V. , Galindo P. , Maestre M. , Zalduendo I.

Studia Mathematica

2004

tom 160

nr 1

83-99

We define the class of integral holomorphic functions over Banach spaces; these are functions admitting an integral representation akin to the Cauchy integral formula, and are related to integral polynomials. After studying various properties of these functions, Banach and Fréchet spaces of integral holomorphic functions are defined, and several aspects investigated: duality, Taylor series approximation, biduality and reflexivity.

Extension of multilinear mappings on Banach spaces

63%

Galindo P. , Garciá D. , Maestre M. , Mujica J.

nr 1

55-76