Supremum norm differentiability
The points of Gateaux and Fréchet differentiability of the norm in C(T,E) are obtained, where T is a locally compact Hausdorff space and E is a real Banach space. Applications of these results are given to the space ℓ∞(E) of all bounded sequences in E and to the space B(ℓ1,E) of all bounded linear o...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171283000605 |
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| _version_ | 1832558982573588480 |
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| author | I. E. Leonard K. F. Taylor |
| author_facet | I. E. Leonard K. F. Taylor |
| author_sort | I. E. Leonard |
| collection | DOAJ |
| description | The points of Gateaux and Fréchet differentiability of the norm in C(T,E) are obtained, where T is a locally compact Hausdorff space and E is a real Banach space. Applications of these results are given to the space ℓ∞(E) of all bounded sequences in E and to the space B(ℓ1,E) of all bounded linear operators from ℓ1 into E |
| format | Article |
| id | doaj-art-14f4f93817584ec385c9b5ee35e5d17b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-14f4f93817584ec385c9b5ee35e5d17b2025-02-03T01:31:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016470571310.1155/S0161171283000605Supremum norm differentiabilityI. E. Leonard0K. F. Taylor1Department of Mathematics, University of Saskatchewan, Saskatoon S7N 0W0, Saskatchewan, CanadaDepartment of Mathematics, University of Saskatchewan, Saskatoon S7N 0W0, Saskatchewan, CanadaThe points of Gateaux and Fréchet differentiability of the norm in C(T,E) are obtained, where T is a locally compact Hausdorff space and E is a real Banach space. Applications of these results are given to the space ℓ∞(E) of all bounded sequences in E and to the space B(ℓ1,E) of all bounded linear operators from ℓ1 into Ehttp://dx.doi.org/10.1155/S0161171283000605Banach spacecontinuos functionsvector-valued functionssupremum normsmooth points. |
| spellingShingle | I. E. Leonard K. F. Taylor Supremum norm differentiability International Journal of Mathematics and Mathematical Sciences Banach space continuos functions vector-valued functions supremum norm smooth points. |
| title | Supremum norm differentiability |
| title_full | Supremum norm differentiability |
| title_fullStr | Supremum norm differentiability |
| title_full_unstemmed | Supremum norm differentiability |
| title_short | Supremum norm differentiability |
| title_sort | supremum norm differentiability |
| topic | Banach space continuos functions vector-valued functions supremum norm smooth points. |
| url | http://dx.doi.org/10.1155/S0161171283000605 |
| work_keys_str_mv | AT ieleonard supremumnormdifferentiability AT kftaylor supremumnormdifferentiability |