Cobos, Fernando and Fernández-Cabrera, Luz M. and Martínez, Antón (2006) Remarks on Compact Operators between Interpolation Spaces associated to Polygons. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas , 100 (1-2). pp. 51-61. ISSN 1578-7303
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Abstract
This note deals with interpolation methods dened by means of polygons. We show necessary and sufcient conditions for compactness of operators acting from a J-space into a K-space.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Interpolation; Banach spaces; compact operators; methods defined by polygons. |
| Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |
| ID Code: | 14991 |
| References: | Beauzamy, B. (1978). Espaces d'Interpolation R´eels: Topologie et G´eom´etrie, Springer, Lecture Notes in Math, 666, Berlin. Bergh, J. & L¨ofstr¨om. (1976). Interpolation spaces. An introduction, Springer, Berlin. Brudny__, Y. and N. Krugljak, N. (1991). Interpolation functors and interpolation spaces, Vol. 1, North- Holland, Amsterdam. Cobos, F. (1994). On the optimality of compactness results for interpolation methods associated to polygons, Indag. Math. 5, 397.401. Cobos, F., Fernández-Cabrera, L.M. and Mart´_nez, A. (2004). Complex interpolation, minimal methods and compact operators, Math. Nachr. 263-264, 67.82. Cobos, F., Fernández-Cabrera, L.M. and Martínez, A. (2005). Compact operators between K- and J-spaces, Studia Math. 166, 199.220. Cobos, F., Fernández-Martínez, P. and Martínez, A. (1999). Measure of non-compactness and interpolation methods associated to polygons, Glasgow Math. J. 41, 65.79. Cobos, F., Fernández-Martínez, P. and Schonbek, T. (1995). Norm estimates for interpolation methods de_ned by means of polygons, J. Approx. Theory, 80, 321.351. 59 F. Cobos, L. M. Fernández-Cabrera, and A. Martínez Cobos, F., Kühn, T. and Schonbek, T. (1992). One-sided compactness results for Aronszajn-Gagliardo functors, J. Funct. Analysis, 106, 274.313. Cobos, F. and Martín, J. (2005). On interpolation of function spaces by methods de_ned by polygons, J. Approx. Theory, 132, 182.203. Cobos, F. and Peetre, J. (1991). Interpolation of compact operators: The multidimensional case, Proc. London Math. Soc. 63, 371.400. Cobos, F. and Romero, R. (2004). Lions-Peetre type compactness results for several Banach spaces, Math. Inequal. Appl. 7, 557.571. Fernandez, D.L. (1979). Interpolation of 2n Banach spaces, Studia Math. 45, 175.201. Fernandez, D.L. (1988). Interpolation of 2d Banach spaces and the Calder´on space X(E). Proc. London Math. Soc. 56, 143.162. Fernández-Cabrera, L.M. (2002). Compact operators between real interpolation spaces, Math. Inequal. & Appl. 5, 283-289. Fernández-Cabrera, L.M. and Mart´_nez, A. (2005). Interpolation methods de_ned by means of polygons and compact operators. Proc. Edinburgh Math. Soc. (to appear). Kalton, N. and Montgomery-Smith, S. (2003). Interpolation of Banach spaces, in Handbook of the geometry of Banach spaces, vol. 2, W.B. Johnson and J. Lindenstrauss, eds, Elsevier, Amsterdam, 1131.1175. Lindenstrauss, J. and Tzafriri, L. (1979). Classical Banach spaces. Function Spaces, vol. 2, Springer, Berlin. Pisier, G. and Xu, Q. (2003). Non-commutative Lp-spaces, in Handbook of the geometry of Banach spaces, vol. 2, W.B. Johnson and J. Lindenstrauss, eds, Elsevier, Amsterdam, 1459.1517. Sparr, G. (1974). Interpolation of several Banach spaces, Ann. Mat. Pura Appl. 99, 247.316. Triebel, H. (1978). Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam |
| Deposited On: | 25 Apr 2012 08:55 |
| Last Modified: | 06 Feb 2014 10:13 |
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