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Swartz type results for nuclear and multiple 1-summing bilinear operators on $$c_{0}\left( \mathcal {X}\right) \times c_{0}\left( \mathcal {Y}\right) $$.
- Source :
- Positivity; Sep2015, Vol. 19 Issue 3, p475-487, 13p
- Publication Year :
- 2015
-
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 $$c_{0}\left( \mathcal {X}\right) $$ . 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13851292
- Volume :
- 19
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Positivity
- Publication Type :
- Academic Journal
- Accession number :
- 109078002
- Full Text :
- https://doi.org/10.1007/s11117-014-0310-8