|
|||||
|
|
Polynomial continuity on |
|
| Authors: | Manuel Gonzá lez Joaquí n M. Gutié rrez José G. Llavona |
| Affiliation: | Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain ; Departamento de Matemáticas, ETS de Ingenieros Industriales, Universidad Politéc- nica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain ; Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain |
| Abstract: | A mapping between Banach spaces is said to be polynomially continuous if its restriction to any bounded set is uniformly continuous for the weak polynomial topology. A Banach space  has property (RP) if given two bounded sequences  , we have that  for every polynomial  on  whenever  for every polynomial  on  ; i.e., the restriction of every polynomial on  to each bounded set is uniformly sequentially continuous for the weak polynomial topology. We show that property (RP) does not imply that every scalar valued polynomial on  must be polynomially continuous. |
| Keywords: | Polynomials on Banach spaces weak polynomial topology polynomials on $ell_1$ |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载全文 | |