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Finite representability of operators in the sense of Bellenot
Author(s):
Manuela
Basallote;
Santiago
Díaz-Madrigal
Journal:
Proc. Amer. Math. Soc.
128
(2000),
3259-3268.
MSC (1991):
Primary 46B07, 46B08
Posted:
April 28, 2000
MathSciNet review:
1707504
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Abstract:
We present several new results about the notion of finite representability of operators introduced by Bellenot.
References:
- [BCD]
- M. Basallote, M. D. Contreras and S. Díaz-Madrigal, Uniformly convexifying operators in classical Banach spaces, to appear in Bull. Austral. Math. Soc. CMP 99:11
- [B]
- B. Beauzamy, Introduction to Banach spaces and their geometry, North-Holland, Amsterdam (1985). MR 88f:46021
- [Be]
- S. F. Bellenot, Local reflexivity of normed spaces, operators, and Fréchet spaces, J. Func. Anal. 59 (1984) 1-11. MR 86a:46011
- [D]
- D. W. Dean, The equation
 and the principle of local reflexivity, Proc. Amer. Math. Soc. 40 (1973) 146-148. MR 48:2735 - [Di]
- J. Diestel, Sequences and series in Banach spaces, Grad. Texts in Math. n. 92, Springer-Verlag, New York, Berlin, Heidelberg (1984). MR 85i:46020
- [GA]
- M. Gonzalez and A. Martínez-Abejón, Supertauberian operators and perturbations, Arch. Math. 64 (1995) 423-433. MR 96m:47022
- [H1]
- S. Heinrich, Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980) 72-104. MR 82b:46013
- [H2]
- S. Heinrich, Finite representability and super-ideals of operators, Dissertationes Mathematicae, Warszawa (1980). MR 81g:47047
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Additional Information:
Manuela
Basallote
Affiliation:
Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, 41092 Sevilla, Spain
Email:
mabas@matinc.us.es
Santiago
Díaz-Madrigal
Affiliation:
Departamento de Matemática Aplicada II, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, 41092 Sevilla, Spain
Email:
madrigal@cica.es
DOI:
10.1090/S0002-9939-00-05548-9
PII:
S 0002-9939(00)05548-9
Received by editor(s):
December 17, 1998
Posted:
April 28, 2000
Additional Notes:
This research has been partially supported by the DGICYT project no. PB97--0706 and by La Consejería de Educación y Ciencia de la Junta de Andalucía.
Communicated by:
David R. Larson
Copyright of article:
Copyright
2000,
American Mathematical Society
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