|
|||||
|
|
Operator ideal norms on |
|
| Authors: | L Rodrí guez-Piazza M C Romero-Moreno |
| Institution: | Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain ; Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain |
| Abstract: | Let  be a real number such that  and its conjugate exponent  . We prove that for an operator  defined on  with values in a Banach space, the image of the unit ball determines whether  belongs to any operator ideal and its operator ideal norm. We also show that this result fails to be true in the remaining cases of  . Finally we prove that when the result holds in finite dimension, the map which associates to the image of the unit ball the operator ideal norm is continuous with respect to the Hausdorff metric. |
| Keywords: | Operator ideals ideal norm $L^p$ spaces Hausdorff metric $p$-integral operators |
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 | |