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Multiple summing operators on$C(K)$spaces

David Pérez-García Departamento de Análisis Matemático Facultad de Matemáticas, Universidad Complutense de Madrid Ignacio Villanueva Departamento de Análisis Matemático Facultad de Matemáticas, Universidad Complutense de Madrid

TBD mathscidoc:1701.333019

Arkiv for Matematik, 42, (1), 153-171, 2003.7
In this paper, we characterize, for 1≤$p$<∞, the multiple ($p$, 1)-summing multilinear operators on the product of$C(K)$spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of ($p$, 1)-summing linear operators on$C(K)$in terms of their representing measures and a new multilinear characterization of$L$_{∞}spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek, and give new results about polymeasures.
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@inproceedings{david2003multiple,
  title={Multiple summing operators on$C(K)$spaces},
  author={David Pérez-García, and Ignacio Villanueva},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203609398203828},
  booktitle={Arkiv for Matematik},
  volume={42},
  number={1},
  pages={153-171},
  year={2003},
}
David Pérez-García, and Ignacio Villanueva. Multiple summing operators on$C(K)$spaces. 2003. Vol. 42. In Arkiv for Matematik. pp.153-171. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203609398203828.
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