A generalization of the Stein-Rosenberg theorem to Banach spaces
In the first part of this note we prove a generalization of the Stein-Rosenberg theorem; the context is that of real Banach spaces with a normal reproducing cone and the operators involved are positive and completely continuous. Our generalization of the Stein-Rosenberg theorem improves the modern v...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0029599X_v34_n4_p403_Milaszewicz |
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| Sumario: | In the first part of this note we prove a generalization of the Stein-Rosenberg theorem; the context is that of real Banach spaces with a normal reproducing cone and the operators involved are positive and completely continuous. Our generalization of the Stein-Rosenberg theorem improves the modern version of it as stated by F. Robert in [5, §2]. In the second part, we discuss briefly how our results are related to other versions of the Stein-Rosenberg theorem. In the last section we describe a situation to which the results in the first part can be applied. © 1980 Springer-Verlag. |
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