New ideals of Bloch mappings which are I-factorizable and Möbius-invariant
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2024-08-09Resumen
In this paper, we introduce a unified method for generating ideals of Möbius-invariant Banach-valued Bloch mappings on the complex open unit disc D, through the composition with the members of a Banach operator ideal I. Using the linearization of derivatives of Banach-valued normalized Bloch mappings on D, this composition method yields the so-called ideals of I-factorizable normalized Bloch mappings I ◦ ˆ B, where ˆ B denotes the class of normalized Bloch mappings on D. We present new examples of them as ideals of separable (Rosenthal, Asplund) normalized Bloch mappings and p-integral (strictly p-integral, p-nuclear) normalized Bloch mappings for any p ∈ [1,∞). Moreover, the Bloch dual ideal I ˆ B-dual of an operator ideal I is introduced and shown that it coincides with the composition ideal Idual ◦ ˆ B.
Palabra/s clave
Bloch mapping
Linearization
Factorization theorems
Operator ideal