Abstract
It is known that an n-homogeneous polynomial is factorable strongly p-summing if and only if its linearization is absolutely p-summing. We prove that a similar result holds for n-linear operators and, as a consequence, we present simplified proofs of recent results from Pellegrino et al. (Rev R Acad Cienc Exactas Fís Nat Ser A Mat RACSAM 110(1):285–302, 2016). Using this connection and the well-known results of the classical linear theory of absolutely p-summing operators we prove other properties for this class of multilinear operators.
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Acknowledgments
We thank the two reviewers for their useful and constructive suggestions and remarks which improve the first version of this paper.
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Popa, D. A note on the concept of factorable strongly p-summing operators. RACSAM 111, 465–471 (2017). https://doi.org/10.1007/s13398-016-0307-1
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DOI: https://doi.org/10.1007/s13398-016-0307-1
Keywords
- Absolutely summing operators
- Strongly summing multilinear mappings
- Nuclear operators
- Projective tensor product