A note on uniformly dominated sets of summing operators
Let Y be a Banach space that has no finite cotype and p a real number satisfying 1≤p<∞. We prove that a set ℳ⊂Πp(X,Y) is uniformly dominated if and only if there exists a constant C>0 such that, for every finite set {(xi,Ti):i=1,…,n}⊂X×ℳ, there is an operator T∈Πp(X,Y) satisfying πp(T)≤C and ‖...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007688 |
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| _version_ | 1832553483526471680 |
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| author | J. M. Delgado C. Piñeiro |
| author_facet | J. M. Delgado C. Piñeiro |
| author_sort | J. M. Delgado |
| collection | DOAJ |
| description | Let Y be a Banach space that has no finite cotype and p a real number satisfying 1≤p<∞. We prove that a set ℳ⊂Πp(X,Y) is uniformly dominated if and
only if there exists a constant C>0 such that, for every finite set {(xi,Ti):i=1,…,n}⊂X×ℳ, there is an operator T∈Πp(X,Y)
satisfying πp(T)≤C and ‖Tixi‖≤‖Txi‖ for i=1,…,n. |
| format | Article |
| id | doaj-art-9136cf93a1134c90995c275cf119774b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9136cf93a1134c90995c275cf119774b2025-02-03T05:53:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129530731210.1155/S0161171202007688A note on uniformly dominated sets of summing operatorsJ. M. Delgado0C. Piñeiro1Departamento de Matemáticas, Escuela Politécnica Superior, Universidad de Huelva, La Rábida 21819, Huelva, SpainDepartamento de Matemáticas, Escuela Politécnica Superior, Universidad de Huelva, La Rábida 21819, Huelva, SpainLet Y be a Banach space that has no finite cotype and p a real number satisfying 1≤p<∞. We prove that a set ℳ⊂Πp(X,Y) is uniformly dominated if and only if there exists a constant C>0 such that, for every finite set {(xi,Ti):i=1,…,n}⊂X×ℳ, there is an operator T∈Πp(X,Y) satisfying πp(T)≤C and ‖Tixi‖≤‖Txi‖ for i=1,…,n.http://dx.doi.org/10.1155/S0161171202007688 |
| spellingShingle | J. M. Delgado C. Piñeiro A note on uniformly dominated sets of summing operators International Journal of Mathematics and Mathematical Sciences |
| title | A note on uniformly dominated sets of summing operators |
| title_full | A note on uniformly dominated sets of summing operators |
| title_fullStr | A note on uniformly dominated sets of summing operators |
| title_full_unstemmed | A note on uniformly dominated sets of summing operators |
| title_short | A note on uniformly dominated sets of summing operators |
| title_sort | note on uniformly dominated sets of summing operators |
| url | http://dx.doi.org/10.1155/S0161171202007688 |
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