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On interpolation of the measure of noncompactness

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2006
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Estonian Academy Publishers
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Abstract
We revised the known results on interpolation of the measure of noncompactness and we announce a new approach to establishing the interpolation formula for the real method.
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Análisis numérico
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1206 Análisis Numérico
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Bergh, J. and Löfström, J. Interpolation Spaces. An Introduction. Springer, Berlin, 1976. Triebel, H. Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam, 1978. Cobos, F., Manzano, A. and Martínez, A. Interpolation theory and measures related to operator ideals. Quart. J. Math., 1999, 50, 401–416. Cobos, F. and Martínez, A. Remarks on interpolation properties of the measure of weak non-compactness and ideal variations. Math. Nachr., 1999, 208, 93–100. Cobos, F., Fernández-Martínez, P. and Martínez, A. Interpolation of the measure of noncompactness by the real method. Studia Math., 1999, 135, 25–38. Schechter, M. Principles of Functional Analysis. American Mathematical Society,Providence, 2002. Cobos, F., Edmunds, D. E. and Potter, A. J. B. Real interpolation and compact linear operators. J. Funct. Anal., 1990, 88, 397–401. Cobos, F. and Fernandez, D. L. On interpolation of compact operators. Ark. Mat., 1989, 27, 211–217. Cobos, F. and Peetre, J. Interpolation of compactness using Aronszajn–Gagliardo functors. Israel J. Math., 1989, 68, 220–240. Cobos, F., Kühn, T. and Schonbek, T. One-sided compactness results for Aronszajn–Gagliardo functors. J. Funct. Anal., 1992, 106, 274–313. Teixeira, M. F. and Edmunds, D. E. Interpolation theory and measure of non-compactness. Math. Nachr., 1981, 104, 129–135. Cobos, F., Fernández-Cabrera, L. M. and Martínez, A. Abstract K and J spaces and measure of non-compactness. Math. Nachr. (to appear). Nilsson, P. Reiteration theorems for real interpolation and approximation spaces. Ann. Mat. Pura Appl., 1982, 132, 291–330.
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https://hdl.handle.net/20.500.14352/50769
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