Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-28T07:52:02.657Z Has data issue: false hasContentIssue false

On duality between K- and J-spaces

Published online by Cambridge University Press:  20 January 2009

Fernando Cobos
Affiliation:
Fernando Cobos, Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain E-mail address: cobos@eucmax.sim.ucm.es
Pedro Fernández-Martínez
Affiliation:
Pedro Fernández-Martínez, Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia, Campus de Espinardo, 30071 Espinardo (Murcia), Spain E-mail address: pedrofdz@fcu.um.es
Antón Martínez
Affiliation:
Antón Martínez Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Industriales, Universidad de Vigo, Lagoas-Marcosende, 36200 Vigo, Spain E-mail address: antonmar@uvigo.es
Yves Raynaud
Affiliation:
Yves Raynaud, Equipe d'Analyse (CNRS), Université Paris, 6 4, Place Jussieu 75252 Paris Cedex 05, France E-mail address: yr@ccr.jussieu.fr
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the relationship between the dual of the K-space defined by means of a polygon and the J-space generated by the dual N-tuple. The results complete the research started in [4]. Special attention is paid to the case when the N-tuple is formed by Banach lattices

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Asekritova, I. and Krugljak, N., On Equivalence of K- and J-methods for (n + 1)-tuples of Banach Spaces, Studia Math. 122 (1997), 99116.Google Scholar
2.Bergh, J. and Löfström, J., Interpolation Spaces. An Introduction (Springer, Berlin–Heidelberg–New York, 1976).CrossRefGoogle Scholar
3.Carro, M. J., Nikolova, L. I., Peetre, J. and Persson, L. E., Some real interpolation methods for families of Banach spaces: A comparison, J Approx. Theory 89 (1997), 2657.CrossRefGoogle Scholar
4.Cobos, F. and Fernádez-Martínez, P., A duality theorem for interpolation methods associated to polygons, Proc. Amer. Math. Soc. 121 (1994), 10931101.CrossRefGoogle Scholar
5.Cobos, F., Fernádez-Martínez, P. and Martínez, A., On reiteration and the behaviour of weak compactness under certain interpolation methods, Collectanea Math., to appear.Google Scholar
6.Cobos, F., Fernádez-Martínez, P. and Schonbek, T., Norm estimates for interpolation methods defined by means of polygons, J. Approx. Theory 80 (1995), 321351.CrossRefGoogle Scholar
7.Cobos, F. and Peetre, J., Interpolation of compact operators: The multidimensional case, Proc. London Math. Soc. 63 (1991), 371400.CrossRefGoogle Scholar
8.Cwikel, M. and Janson, S., Real and complex interpolation methods for finite and infinite families of Banach spaces, Adv. Math. 66 (1987), 234290.CrossRefGoogle Scholar
9.Dore, G., Guidetti, D. and Venni, A., Some properties of the sum and intersection of normed spaces, Atti Sem. Mat. Fis. Univ. Modena 31 (1982), 325331.Google Scholar
10.Favini, A., Su una estensione del metodo d'interpolazione complesso, Rend. Semin. Mat. Univ. Padova 47 (1972), 243298.Google Scholar
11.Fernandez, D. L., Interpolation of 2d Banach spaces and the Calderón spaces X(E), Proc. London Math. Soc. 56 (1988), 143162.CrossRefGoogle Scholar
12.Meyer-Nieberg, P., Banach Lattices (Springer-Verlag, Berlin, 1991).CrossRefGoogle Scholar
13.Persson, A., Compact linear mappings between interpolation spaces, Arkiv. Mat. 5 (1964), 215219.CrossRefGoogle Scholar
14.Sparr, G., Interpolation of several Banach spaces, Ann. Mat. Pura Appl. 99 (1974), 247316.CrossRefGoogle Scholar
15.Teixeira, M. F. and Edmunds, D. E., Interpolation theory and measure of non-compactness, Math. Nachr. 104 (1981), 129135.CrossRefGoogle Scholar
16.Vulikh, B. Z. and Lozanovskii, G. Ya., On the representation of completely linear and regular functionals in partially ordered spaces, Math. USSR-Sb. 13 (1971), 323343.CrossRefGoogle Scholar