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

Swartz type results for nuclear and multiple 1-summing bilinear operators on $$c_{0}\left(... In this paper we investigate the bilinear versions of Swartz’s theorem. Thus we characterize the nuclear and the multiple 1-summing operators on a cartesian product of $$c_{0}\left( \mathcal {X}\right) $$ c 0 X . As applications we give the necessary and sufficient conditions for some natural operators on a cartesian product of $$c_{0}\left( \mathcal {X}\right) $$ c 0 X 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

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

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Publisher
Springer Basel
Copyright
Copyright © 2014 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-014-0310-8
Publisher site
See Article on Publisher Site

Abstract

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 $$c_{0}\left( \mathcal {X}\right) $$ c 0 X . As applications we give the necessary and sufficient conditions for some natural operators on a cartesian product of $$c_{0}\left( \mathcal {X}\right) $$ c 0 X 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.

Journal

PositivitySpringer Journals

Published: Oct 1, 2014

References

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