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We characterize the norm attaining bilinear forms on L1[0,1], and show that the set of norm attaining ones is not dense in the space of continuous bilinear forms on L1[0,1].
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
for polynomials P: X → X. We show that this equation holds for every polynomial on the complex space X =...
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