Artículo
Milaszewicz, J.P. "A generalization of the Stein-Rosenberg theorem to Banach spaces" (1980) Numerische Mathematik. 34(4):403-409
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Abstract:
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.
Registro:
| Documento: | Artículo |
| Título: | A generalization of the Stein-Rosenberg theorem to Banach spaces |
| Autor: | Milaszewicz, J.P. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Buenos Aires, 1428, Argentina |
| Palabras clave: | Subject Classifications: AMS(MOS):65F10, 47B55, CR: 5.14 |
| Año: | 1980 |
| Volumen: | 34 |
| Número: | 4 |
| Página de inicio: | 403 |
| Página de fin: | 409 |
| DOI: | http://dx.doi.org/10.1007/BF01403677 |
| Título revista: | Numerische Mathematik |
| Título revista abreviado: | Numer. Math. |
| ISSN: | 0029599X |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0029599X_v34_n4_p403_Milaszewicz |
Referencias:
- Birkhoff, G., Varga, R.S., Reactor criticality and nonnegative matrices (1958) Journal of the Society for Industrial and Applied Mathematics, 6, pp. 354-377
- Fiedler, M., Pták, V., Über die Konvergenz des verallgemeinerten Seidelschen Verfahrens zur Lösung von Systemen linearer Gleichungen (1956) Mathematische Nachrichten, 15, pp. 31-38
- Krein, M.G., Rutman, M.A., Linear operators leaving invariant a cone in a Banach space (1962) Translations of the A.M.S., 10, pp. 199-325
- Marek, I., u<inf>0</inf>-positive operators and some of their applications (1967) SIAM Journal on Applied Mathematics, 15, pp. 484-494
- Robert, F., Autour du théorème de Stein-Rosenberg (1976) Numer. Math., 27, pp. 133-141
- Stein, P., Rosenberg, R.L., On the solution of linear simultaneous equations by iteration (1948) Journal of the London Mathematical Society, 23, pp. 111-118
- Vandergraft, J.S., Spectral properties of matrices which have invariant cones (1968) SIAM Journal on Applied Mathematics, 16, pp. 1208-1222
- Varga, R.S., (1962) Matrix iterative analysis, , Prentice-Hall, Englewood Cliffs, N.J
Citas:
---------- APA ----------
(1980) . A generalization of the Stein-Rosenberg theorem to Banach spaces. Numerische Mathematik, 34(4), 403-409.http://dx.doi.org/10.1007/BF01403677
---------- CHICAGO ----------
Milaszewicz, J.P. "A generalization of the Stein-Rosenberg theorem to Banach spaces" . Numerische Mathematik 34, no. 4 (1980) : 403-409.http://dx.doi.org/10.1007/BF01403677
---------- MLA ----------
Milaszewicz, J.P. "A generalization of the Stein-Rosenberg theorem to Banach spaces" . Numerische Mathematik, vol. 34, no. 4, 1980, pp. 403-409.http://dx.doi.org/10.1007/BF01403677
---------- VANCOUVER ----------
Milaszewicz, J.P. A generalization of the Stein-Rosenberg theorem to Banach spaces. Numer. Math. 1980;34(4):403-409.http://dx.doi.org/10.1007/BF01403677
