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Unconditionally Converging Multilinear Operators

Fernando Bombal, Maite Fernández-Unzueta, Ignacio Villanueva

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Abstract

We introduce a notion of unconditionally converging multilinear operator which allows to extend many of the results of the linear case to the multilinear case. We prove several characterizations of these multilinear operators (one of which seems to be new also in the linear case), which allow to considerably simplify the work with this kind of operators.

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What this paper is about

We introduce a notion of unconditionally converging multilinear operator which allows to extend many of the results of the linear case to the multilinear case. We prove several characterizations of these multilinear operators (one of which seems to be new also in the linear case), which allow to considerably simplify the work with this kind of operators.

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Available abstract

We introduce a notion of unconditionally converging multilinear operator which allows to extend many of the results of the linear case to the multilinear case. We prove several characterizations of these multilinear operators (one of which seems to be new also in the linear case), which allow to considerably simplify the work with this kind of operators.

Key concepts: Multilinear map, Mathematics, Operator (biology), Linear operators, Algebra over a field, Applied mathematics, Pure mathematics, Mathematical analysis

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