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Nuclear multilinear operators with respect to a partition

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Abstract

We introduce the notion of multilinear nuclear operator with respect to a partition and extend Grothendieck’s characterizations of nuclear linear operators into \(l_{1},\) resp. \(L_{1}( \mu ),\) in this new setting. We give the necessary and sufficient conditions for a natural operator to be nuclear with respect to a partition.

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Acknowledgments

We would like to express our gratitude to the referee for many valuable comments and suggestions which have improved the final version of the paper.

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  1. Department of Mathematics, Ovidius University of Constanta, Bd. Mamaia 124, 900527, Constanta, Romania

    Dumitru Popa

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  1. Dumitru Popa
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Correspondence to Dumitru Popa.

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Popa, D. Nuclear multilinear operators with respect to a partition. Rend. Circ. Mat. Palermo 61, 307–319 (2012). https://doi.org/10.1007/s12215-012-0091-5

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  • DOI: https://doi.org/10.1007/s12215-012-0091-5

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