Cohen strongly p-summing holomorphic mappings on Banach spaces

Abstract

Let E and F be complex Banach spaces, U be an open subset of E and 1le ple infty . We introduce and study the notion of a Cohen strongly p-summing holomorphic mapping from U to F, a holomorphic version of a strongly p-summing linear operator. For such mappings, we establish both Pietsch Domination/Factorization Theorems and analyse their linearizations from (the canonical predual of ) and their transpositions on Concerning the space formed by such mappings and endowed with a natural norm we show that it is a regular Banach ideal of bounded holomorphic mappings generated by composition with the ideal of strongly p-summing linear operators. Moreover, we identify the space with the dual of the completion of tensor product space endowed with the Chevet–Saphar norm g_p.