Cohen strongly p-summing holomorphic mappings on Banach spaces

2022/09/07 by Jiménez-Vargas, A., Saadi, K., Sepulcre, J. M.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2209.03038

Abstract

Let E and F be complex Banach spaces, U be an open subset of E and 1≤ p≤∞. 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 G^∞(U) (the canonical predual of H^∞(U)) and their transpositions on H^∞(U). Concerning the space D_p^{H^∞}(U,F) formed by such mappings and endowed with a natural norm d_p^{H^∞}, 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 (D_p^{H^∞}(U,F^*),d_p^{H^∞}) with the dual of the completion of tensor product space G^∞(U)⊗ F endowed with the Chevet--Saphar norm g_p.

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