Lipschitz p-summing multilinear operators correspond to Lipschitz p-summing operators

2022/04/04 by Fernández-Unzueta, Maite
#46B28 #46T99 #47H60 #47L22 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2204.01775

Abstract

We give conditions that ensure that an operator satisfying a Piestch domination in a given setting also satisfies a Piestch domination in a different setting. From this we derive that a bounded mutlilinear operator T is Lipschitz p-summing if and only if the mapping f_T(x₁⊗⋯ ⊗ x_n):=T(x₁,…, x_n) is Lipschitz p-summing. The results are based on the projective tensor norm. An example with the Hilbert tensor norm is provided to show that the statement may not hold when a reasonable cross-norm other than the projective tensor norm is considered.

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