Une caracterisation de la proprieté de Radon-Nikodym analytique pour les espaces de Banach isomorphes a leur carrés. (A characterization of the analytic Radon-Nikodym property for Banach spaces isomorphic to their squares)
We prove that if a complex Banach space isomorphic to its square fails the analytic Radon-Nikodym property, then there exists a bounded analytic regular and injective F: \({\mathbb{D}}\mapsto X\), there exists \(c>0\) and a sequence \((r_ n)_{n\geq 0}\) of radii strictly increasing to 1, such that \(\| F(re^{it})-F(r'e^{is})\| \geq c,\) for all \((t,s)\in [0,2\pi]^ 2,\) all \(r\leq r_ n\), all \(r'\geq r_{n+1}\), and all \(n\geq 0\). We obtain a new characterization of analytic Radon-Nikodym property in complex Banach spaces isomorphic to their square, by means of holomorphic embeddings of the open unit disk. This solves a problem of Aurich in these spaces.
complex Banach space isomorphic to its square
holomorphic embeddings of the open unit disk
scientific article; zbMATH DE number 4146836