Symmetric ideals of generalized summing multilinear operators

2023/06/20 by Botelho, Geraldo, Santiago, Ariel S.
#46G25 #47B10 #47H60 #47L22 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2306.11860

Abstract

Let X₁, …, X_n,Y be classes of Banach spaces-valued sequences. An n-linear operator A between Banach spaces belongs to the ideal of (X₁, …, X_n;Y)-summing multilinear operators if (A(x_j¹, …, x_jⁿ))_j=1^∞ belongs to Y whenever (x_j^k)_{j= 1}^∞ belongs to X_k, k = 1, …, n. In this paper we develop techniques to generate non trivial symmetric ideals of this type. Illustrative examples and additional applications of the techniques are provided.

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