Daugavet property of Banach algebras of holomorphic functions and norm-attaining holomorphic functions
We show that the duals of Banach algebras of scalar-valued bounded holomorphic functions on the open unit ball BE of a Banach space E lack weak⁎-strongly exposed points. Consequently, we obtain that some Banach algebras of holomorphic functions on an arbitrary Banach space have the Daugavet property...
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Veröffentlicht in: | Advances in mathematics (New York. 1965) 2023-05, Vol.421, p.109005, Article 109005 |
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Sprache: | eng |
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Zusammenfassung: | We show that the duals of Banach algebras of scalar-valued bounded holomorphic functions on the open unit ball BE of a Banach space E lack weak⁎-strongly exposed points. Consequently, we obtain that some Banach algebras of holomorphic functions on an arbitrary Banach space have the Daugavet property which extends the observation of P. Wojtaszczyk [56]. Moreover, we present a new denseness result by proving that the set of norm-attaining vector-valued holomorphic functions on the open unit ball of a dual Banach space is dense provided that its predual space has the metric π-property. Besides, we obtain several equivalent statements for the Banach space of vector-valued homogeneous polynomials to be reflexive, which improves the result of J. Mujica [47], J. A. Jaramillo and L. A. Moraes [39]. As a byproduct, we generalize some results on polynomial reflexivity due to J. Farmer [35]. |
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ISSN: | 0001-8708 1090-2082 |
DOI: | 10.1016/j.aim.2023.109005 |