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Measure of non-compactness and interpolation methods associated to polygons

Cobos, Fernando and Fernández-Martínez, Pedro and Martínez, Antón (1999) Measure of non-compactness and interpolation methods associated to polygons. Glasgow Mathematical Journal, 41 (1). pp. 65-79. ISSN 0017-0895

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We establish an estimate for the measure of non-compactness of an
interpolated operator acting from a J-space into a K-space. Our result refers to
general Banach N-tuples. We also derive estimates for entropy numbers if some of
the N-tuples reduce to a single Banach space.

Item Type:Article
Uncontrolled Keywords:Measure of Non-Compactness; Interpolated Operator Acting from A J-Space into A K-Space; Entropy Numbers
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15277

J. Bergh and J. Löfström, Interpolation spaces, an introduction (Springer-Verlag,1976).

B. Carl and I. Stephani, Entropy, compactness and the approximation of operators(Cambridge University Press, 1990).

F. Cobos, On optimality of compactness results for interpolation methods associated to polygons, Indag. Math. 5 (1994), 397±401.

F. Cobos, P. Fernández-Martínez and A. Martínez, On reiteration and the behaviour of weak compactness under certain interpolation methods, Collect. Math., to appear.

F. Cobos, P. Fernández-Martínez and A. Martínez, Interpolation of the measure of non-compactness by the real method, Studia. Math., to appear.

F. Cobos, P. Fernández-Martinez and T. Schonbek, Norm estimates for interpolation methods de®ned by means of polygons, J. Approx. Theory 80 (1995), 321±351.

F. Cobos, T. KuÈ hn and T. Schonbek, One-sided compactness results for Aronszajn Gagliardo functors, J. Functional Analysis 106 (1992), 274±313.

F. Cobos and J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. 63 (1991), 371±400.

D. E. Edmunds and W. D. Evans, Spectral theory anddifferential operators (Clarendon Press, Oxford, 1987).

F. Cobos, P. Fernández-Martínez and A. Martínez

L. I. Nikolova, Some estimates of measure of non-compactness for operators acting in interpolation spaces Ð the multidimensional case, C.R. Acad. Bulg. Sci. 44 (1991), 5±8.

A. Pietsch, Operator ideals (North-Holland, Amsterdam, 1980).

M. F. Teixeira and D. E. Edmunds, Interpolation theory and measures of non-compactness, Math. Nachr. 104 (1981), 129±135.

H. Triebel, Interpolation theory, function spaces, differential operators (North-Holland Amsterdam, 1978).

Deposited On:21 May 2012 10:39
Last Modified:06 Feb 2014 10:20

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