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Finite representability of operators in the sense of Bellenot


Authors: Manuela Basallote and Santiago Díaz-Madrigal
Journal: Proc. Amer. Math. Soc. 128 (2000), 3259-3268
MSC (1991): Primary 46B07, 46B08
DOI: https://doi.org/10.1090/S0002-9939-00-05548-9
Published electronically: 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 [Enhancements On Off] (What's this?)

  • [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 $L(E,X^{**})=L(E,X)^{**}$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: https://doi.org/10.1090/S0002-9939-00-05548-9
Received by editor(s): December 17, 1998
Published electronically: 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
Article copyright: © Copyright 2000 American Mathematical Society

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