p-Compactness of Bloch maps

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 D⊆ C D ⊆ 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 D D , inclusion properties, factorisation of their derivatives, and transposition on the normalized Bloch space. We also present right p -nuclear Bloch maps of D D to X and study its relation with p -compact Bloch maps.