### Impacto

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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Official URL: http://journals.cambridge.org/download.php?file=%2FGMJ%2FGMJ41_01%2FS0017089599970404a.pdf&code=4690f1c1

## Abstract

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 |
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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 |

References: | 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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