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Abstract K and J Spaces and Measure of Non-Compactness

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2007
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Wiley-VCH Verlag Gmbh
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We establish a formula for the measure of non-compactness of an operator interpolated by the general real method generated by a sequence lattice Γ. The formula is given in terms of the norms of the shift operators in Γ.
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[1] J. Bergh and J. L¨ofstr¨om, Interpolation Spaces. An Introduction (Springer-Verlag, Berlin, 1976). [2] E. Brandani da Silva and D. L. Fernandez, Interpolation spaces with function parameter and measures of noncompactness, Lobachevskii J. Math. 9, 15–27 (2001). [3] Y. Brudnyˇı and N. Krugljak, Interpolation Functors and Interpolation Spaces, Vol. 1 (North-Holland, Amsterdam, 1991). [4] B. Carl and I. Stephani, Entropy, Compactness and the Approximation of Operators (Cambridge Univ. Press, Cambridge, 1990). [5] F. Cobos, M. Cwikel, and P. Matos, Best possible compactness results of Lions-Peetre type, Proc. Edinb. Math. Soc., II Ser. 44, 153–172 (2001). [6] F. Cobos, D. E. Edmunds, and A. J. B. Potter, Real interpolation and compact linear operators, J. Funct. Anal. 88, 351–365 (1990). [7] F. Cobos and D. L. Fernandez, On interpolation of compact operators, Ark. Mat. 27, 211–217 (1989). [8] F. Cobos, L. M. Fern´andez–Cabrera, and A. Mart´ınez, Compact operators between K- and J-spaces, Studia Math. 166, 199–220 (2005). www.mn-journal.com _c 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1708 Cobos, Fern´andez–Cabrera, and Mart´ınez: Measure of non-compactness [9] F. Cobos, P. Fern´andez–Mart´ınez, and A.Mart´ınez, Interpolation of the measure of non-compactness by the real method, Studia Math. 135, 25–38 (1999). [10] F. Cobos, T. K¨uhn, and T. Schonbek, One-sided compactness results for Aronszajn–Gagliardo functors, J. Funct. Anal. 106, 274–313 (1992). [11] F. Cobos and J. Peetre, Interpolation of compactness using Aronszajn–Gagliardo functors, Israel J. Math. 68, 220–240 (1989). [12] J. M. Cordeiro, Interpolaci´on de Ciertas Clases de Operadores por M´etodos Multidimensionales, Ph.D. thesis, Publicaciones del Depto. de Matem´atica Aplicada, Universidad de Vigo (1999). [13] M. Cwikel and J. Peetre, Abstract K and J spaces, J. Math. Pures Appl. (9) 60, 1–50 (1981). [14] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators (Clarendon Press, Oxford 1987). [15] W. D. Evans and B. Opic, Real interpolation with logarithmic functors and reiteration, Canad. J. Math. 52, 920–960 (2000). [16] W. D. Evans, B. Opic, and L. Pick, Real Interpolation with logarithmic functors, J. Inequal. Appl. 7, 187–269 (2002). [17] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42, 289–305 (1978). [18] J. Gustavsson and J. Peetre, Interpolation of Orlicz spaces, Studia Math. 60, 33–59 (1977). [19] S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44, 50–73 (1981). [20] A. Lebow and M. Schechter, Semigroups of operators and measures of noncompactness, J. Funct. Anal. 7, 1–26 (1971). [21] C. Merucci, Interpolation r´eele avec parametre fonctionnel des espaces Lp,q, C. R. Math. Acad. Sci. Paris 294, 653–656 (1982). [22] P. Nilsson, Reiteration theorems for real interpolation and approximation spaces, Ann. Mat. Pura Appl. (4) 132, 291–330 (1982). [23] P. Nilsson, Interpolation of Calder´on and Ovchinnikov pairs, Ann. Mat. Pura Appl. (4) 134, 201–332 (1983). [24] J. Peetre, A theory of interpolation of normed spaces, Notas de Matem´atica No. 39 (Instituto de Matem´atica Pura e Aplicada, Conselho National de Pesquisas, Rio de Janeiro, 1968). [25] L. E. Persson, Interpolation with a parameter function, Math. Scand. 59, 199–222 (1986). [26] R. Szwedek, Measure of non-compactness of operators interpolated by real method, Studia Math. 175, 157–174 (2006). [27] M. F. Teixeira and D. E. Edmunds, Interpolation theory and measures of non-compactness, Math. Nachr. 104, 129–135 (1981). [28] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators (North-Holland, Amsterdam, 1978).
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