Nuclear multilinear operators with respect to a partition |
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Authors: | Dumitru Popa |
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Institution: | 1. Department of Mathematics, Ovidius University of Constanta, Bd. Mamaia 124, 900527, Constanta, Romania
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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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