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arXiv · 2112.12829

Regularity of the coefficients of multilinear forms on sequence spaces

Daniel Pellegrino·Anselmo Raposo Jr·Diana Serrano-Rodríguez
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Abstract

The investigation of regularity/summability properties of the coefficients of bilinear forms in sequence spaces was initiated by Littlewood in $1930$. Nowadays, this topic has important connections with other fields of Pure and Applied Mathematics as Complex Analysis, Quantum Information Theory, Theoretical Computer Science and Combinatorial Games. In this paper we explore a regularity technique to obtain optimal parameters for several results in this framework, extending/generalizing theorems of Osikiewicz and Tonge ($2001$), Albuquerque \textit{et al.} ($2016$), Aron \textit{et al.} ($2017$), Albuquerque and Rezende ($2018$), Paulino ($2020$), among others.

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Daniel Pellegrino, Anselmo Raposo Jr, Diana Serrano-Rodríguez. 2021-12-23. Regularity of the coefficients of multilinear forms on sequence spaces. https://arxiv.org/abs/2112.12829

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