Daugavet property of Banach algebras of holomorphic functions and norm-attaining holomorphic functions

We show that the duals of Banach algebras scalar-valued bounded holomorphic functions on open unit ball BE a space E lack weak⁎-strongly exposed points. Consequently, we obtain some an arbitrary have Daugavet property which extends observation P. Wojtaszczyk [56]. Moreover, present new denseness result by proving set norm-attaining vector-valued dual is dense provided its predual has metric π-property. Besides, several equivalent statements for homogeneous polynomials to be reflexive, improves J. Mujica [47], A. Jaramillo and L. Moraes [39]. As byproduct, generalize results polynomial reflexivity due Farmer [35].