Weighted holomorphicmappings attaining their norms
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Jiménez Vargas, AntonioFecha
2023-08-22Resumen
Given an open subset U of C^n, a weight v on U and a complex Banach space F, let H_v(U, F) denote the Banach space of all weighted holomorphic mappings f : U →F, under the weighted supremum norm ||f||_v=:= sup {v(z)||f (z)||: z ∈ U}. We prove that the set of all mappings f ∈ H_v(U, F) that attain their weighted supremum norms is norm dense in Hv(U, F), provided that the closed unit ball of the little weighted holomorphic space H_{v_0} (U, F) is compact-open dense in the closed unit ball of H_v(U, F). We also prove a similar result for mappings f ∈ H_v(U, F) such that vf has a relatively compact range.
Palabra/s clave
Matemáticas
Holomorphic function
Norm attaining operator
Radon–Nikodým property