New ideals of Bloch mappings which are I-factorizable and Möbius-invariant

In this paper, we introduce an unified method for generating ideals of Möbius-invariant Banach-valued Bloch mappings on the complex open unit disc , through the composition with the members of a Banach operator ideal . Using linearisation of derivatives of Banach-valued normalized Bloch mappings on , this composition method yields the so-called ideals of -factorizable normalized Bloch mappings ∘̂, where ̂ denotes the class of normalized Bloch mappings on . 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 ̂- of an operator ideal is introduced and shown that it coincides with the composition ideal ^∘̂.