p-Compactness of Bloch maps

Abstract

Influenced by the concept of a p-compact operator due to Sinha and Karn (Stud Math 150(1): 17–33, 2002), we introduce p-compact Bloch maps of the open unit disk \(\mathbb {D}\subseteq \mathbb {C}\) to a complex Banach space X, and obtain its most outstanding properties: surjective Banach ideal property, Möbius invariance, linearisation on the Bloch-free Banach space over \(\mathbb {D}\), inclusion properties, factorisation of their derivatives, and transposition on the normalized Bloch space. We also present right p-nuclear Bloch maps of \(\mathbb {D}\) to X and study its relation with p-compact Bloch maps.