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Positivity

, Volume 18, Issue 1, pp 29–39 | Cite as

Remarks on multiple summing operators on \(C(\Omega )\)-spaces

Article

Abstract

We give the necessary and sufficient conditions for a multilinear bounded operator on \(C(\Omega _{1}) \times \cdots \times C(\Omega _{k}) \times X_{k+1}\times \cdots \times X_{k+n}\) to be multiple 1-summing. Based on this result we prove an inclusion result for multiple summing operators and an unexpected composition result of Grothendieck type for bilinear operators.

Keywords

\(p\)-summing operators Multiple \(p\)-summing operators  Nuclear operators Banach spaces of continuous functions 

Mathematics Subject Classification (2010)

Primary 47H60 ; Secondary 47B10 47L20 46G10 

Notes

Acknowledgments

We would like to express our gratitude to the referee for his/her very careful reading of the manuscript, many valuable comments, suggestions which have improved the final version of the paper.

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of MathematicsOvidius University of ConstantaConstantaRomania

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