Abstract
We give the necessary and sufficient conditions for bounded multilinear operators on \(X_{1}\times \cdots \times X_{k}\times c_{0}\) to be nuclear or multiple 1-summing. We find the necessary and sufficient conditions for some bounded bilinear operators from \(l_{p}\times c_{0}\) into Y to be nuclear or multiple 1-summing operators. In the case of some bounded bilinear operators from \(l_{p}\times c_{0}\) into \(c_{0}\) associated to the classical methods of summability, we find the necessary and sufficient conditions for these be nuclear or multiple 1-summing operators. We show that, contrary to the bilinear case, in the multilinear case the situation change.
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Communicated by Miklós Pálfia.
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Popa, D. Nuclear and multiple 1-summing operators on \(X_{1}\times \cdots \times X_{k}\times c_{0}\). Banach J. Math. Anal. 16, 66 (2022). https://doi.org/10.1007/s43037-022-00218-1
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DOI: https://doi.org/10.1007/s43037-022-00218-1
Keywords
- p-Summing operators
- Nuclear operators
- Multiple 1-summing operators
- Method of summability
- Multiplication operator