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Numerische Mathematik

, Volume 34, Issue 4, pp 403–409 | Cite as

A generalization of the Stein-Rosenberg theorem to Banach spaces

  • J. P. Milaszewicz
Article

Summary

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.

Subject Classifications

AMS(MOS):65F 10, 47B 55 CR: 5.14 

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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • J. P. Milaszewicz
    • 1
  1. 1.Departamento de Matemática, Facultad de Ciencias Exactas y NaturalesCiudad UniversitariaBuenos AiresArgentina

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