, Volume 19, Issue 3, pp 475–487 | Cite as

Swartz type results for nuclear and multiple 1-summing bilinear operators on \(c_{0}\left( \mathcal {X}\right) \times c_{0}\left( \mathcal {Y}\right) \)

  • Gabriela Badea
  • Dumitru Popa


In this paper we investigate the bilinear versions of Swartz’s theorem. Thus we characterize the nuclear and the multiple 1-summing operators on a cartesian product of \(c_{0}\left( \mathcal {X}\right) \). As applications we give the necessary and sufficient conditions for some natural operators on a cartesian product of \(c_{0}\left( \mathcal {X}\right) \) to be multiple 1-summing and nuclear operators. By an example, we show that the natural bilinear version of Swartz’s theorem is not necessarily true.


Multiple 1-summing bilinear operators Nuclear operators  Swartz’s Theorem 

Mathematics Subject Classification

Primary 47B10 47L20 Secondary 46B45 



We thank the referee for his/her carefully reading of the manuscript and useful suggestions which have improved the quality of the presentation.


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringOvidius University of ConstantaConstantaRomania
  2. 2.Department of MathematicsOvidius University of ConstantaConstantaRomania

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