Absolutely summing multilinear operators: a panorama
Daniel Pellegrino, Joedson Santos
TL;DR
This paper reviews the theory of absolutely summing operators and their multilinear generalizations, aiming to identify optimal extensions and outline open problems for future research in the field.
Contribution
It provides a comprehensive overview of absolutely summing multilinear operators and initiates a research project to find ideal extensions of these operators.
Findings
Summarizes current state of multilinear absolutely summing operators
Proposes a framework for identifying 'perfect' operator extensions
Highlights open problems for future exploration
Abstract
This paper has a twofold purpose: to present an overview of the theory of absolutely summing operators and its different generalizations for the multilinear setting, and to sketch the beginning of a research project related to an objective search of \textquotedblleft perfect\textquotedblright \ multilinear extensions of the ideal of absolutely summing operators. The final section contains some open problems that may indicate lines for future investigation.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Holomorphic and Operator Theory