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Abstract K and J Spaces and Measure of Non-Compactness


Cobos, Fernando and Fernández-Cabrera, Luz M. and Martínez, Antón (2007) Abstract K and J Spaces and Measure of Non-Compactness. Mathematische Nachrichten, 280 (15). pp. 1698-1708. ISSN 0025-584X

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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.

Item Type:Article
Uncontrolled Keywords: Aronszajn-Gagliardo Functors; Real Interpolation; Logarithmic Functors; Function Parameter; Real interpolation; interpolation with a parameter function; measure of non-compactness; Mathematics
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:14978

[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). _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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