Besoy, Blanca F.Cobos, Fernando2023-06-162023-06-162020[1] W. Amrein, A. Boutet de Monvel and V. Georgescu, C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Springer, Basel, 1996. [2] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988. [3] C. Bennett and K. Rudnick, On Lorentz-Zygmund spaces, Dissertationes Math. 175 (1980), 1-72. [4] J. Bergh and J. L�ofstr�om, Interpolation Spaces. An introduction, Springer, Berlin, 1976. [5] B.F. Besoy, On compactness theorems for logarithmic interpolation methods, Proceedings of the Conference Function Spaces XII, Banach Center Publ. (to appear). [6] B.F. Besoy and F. Cobos, Duality for logarithmic interpolation spaces when 0 < q < 1 and applications, J. Math. Anal. Appl. 466 (2018), 373-399. [7] B.F. Besoy and F. Cobos, Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces, J. Approx. Theory 243 (2019), 25-44. [8] Y. Brudny�� and N. Krugljak, Interpolation Functors and Interpolation Spaces, Vol. 1, North-Holland, Amsterdam, 1991. [9] P.L. Butzer and H. Berens, Semi-Groups of Operators and Approximation, Springer-Verlag, Berlin, 1967. [10] A.P. Calder�on, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113{190. [11] F. Cobos, Interpolation theory and compactness, in Function Spaces, Inequalities and Interpolation. Edited by J. Lukes and L. Pick, Paseky, Prague 2009, pp. 31-75. [12] F. Cobos, L.M. Fern�andez-Cabrera and A. Mart��nez, Abstract K and J spaces and measure of non-compactness, Math. Nachr. 280 (2007), 1698-1708. [13] F. Cobos, L.M. Fern�andez-Cabrera and A. Mart��nez, On a paper of Edmunds and Opic on limiting interpolation of compact operators between Lp spaces, Math. Nachr. 288 (2015), 167-175. [14] F. Cobos, L.M. Fern�andez-Cabrera and A. Mart��nez, Measure of non-compactness of operators interpolated by limiting real methods, in Operator Theory: Advances and Applications, 219, Springer, Basel 2012, pp. 37{54. [15] F. Cobos, L.M. Fern�andez-Cabrera and A. Mart��nez, Estimates for the spectrum on logarithmic interpolation spaces, J. Math. Anal. Appl. 437 (2016), 292-309. [16] F. Cobos, L.M. Fern�andez-Cabrera, T. K�uhn and T. Ullrich, On an extreme class of real interpolation spaces, J. Funct. Anal. 256 (2009), 2321-2366. [17] F. Cobos, P. Fern�andez-Mart��nez and A. Mart��nez, Interpolation of the measure of non-compactnes by the real method, Studia Math. 135 (1999), 25-38. [18] F. Cobos, T. K�uhn and T. Schonbek, One-sided compactness results for Aronszajn-Gagliardo functors, J. Funct. Anal. 106 (1992), 274-313. [19] F. Cobos and J. Peetre, Interpolation of compactness using Aronszajn-Gagliardo functors, Israel J. Math. 68 (1989), 220-240. [20] F. Cobos and A. Segurado, Description of logarithmic interpolation spaces by means of the J- functional and applications, J. Funct. Anal. 268 (2015), 2906-2945. [21] A. Connes, Noncommutative Geometry, Academic Press, San Diego, 1994. [22] 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. [23] M. Cwikel, Real and complex interpolation and extrapolation of compact operators, Duke Math. J. 65 (1992), 333-343. [24] R.Ya. Doktorskii, Reiteration relations of the real interpolation method, Soviet Math. Dokl. 44 (1992), 665-669. [25] D.E. Edmunds and W.D. Evans, Hardy Operators, Function Spaces and Embeddings, Springer, Berlin 2004. [26] D.E. Edmunds and Yu. Netrusov, Entropy numbers and interpolation, Math. Ann. 351 (2011), 963-977. [27] D.E. Edmunds and Yu. Netrusov, Entropy numbers of operators acting between vector-valued sequence spaces, Math. Nachr. 286 (2013), 614-630. [28] D.E. Edmunds and B. Opic, Limiting variants of Krasnoselski��'s compact interpolation theorem, J. Funct. Anal. 266 (2014), 3265-3285. [29] W.D. Evans and B. Opic, Real interpolation with logarithmic functors and reiteration, Canad. J. Math. 52 (2000), 920-960. [30] W.D. Evans, B. Opic and L. Pick, Real interpolation with logarithmic functors, J. Inequal. Appl. 7 (2002), 187-269. [31] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289-305. [32] H. K�onig, Eigenvalue Distribution of Compact Operators, Birkh�auser, Basel, 1986. [33] G. K�othe, Topological Vector Spaces I, Springer, Berlin, 1969. [34] M.A. Krasnosel'ski��, On a theorem of M. Riesz, Dokl. Akad. Nauk SSSR. 131 (1960), 246-248. [35] J.L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Publ. Math. Inst. Hautes Etudes Sci. 19 (1964), 5-68. [36] M. Masty lo and E.B. Silva, Interpolation of the measure of non-compactness of bilinear operators, Trans. Amer. Math. Soc. 370 (2018), 8979-8997. [37] P. Nilsson, Reiteration theorems for real interpolation and approximation spaces, Ann. Mat. Pura Appl. 132 (1982), 291-330. [38] B. Opic and L. Pick, On generalized Lorentz-Zygmund spaces, Math. Inequal. Appl. 2 (1999), 391- 467. [39] L.E. Persson, Interpolation with a parameter function, Math. Scand. 59 (1986), 199-222. [40] M. Schechter, Principles of Functional Analysis, Amer. Math. Soc., Providence, 2001. [41] R. Szwedek, Measure of non-compactness of operators interpolated by the real method, Studia Math. 175 (2006), 157-174. [42] R. Szwedek, On interpolation of the measure of non-compactness by the complex method, Quart. J. Math. Oxford 66 (2015), 323-332. [43] R. Szwedek, Geometric interpolation of entropy numbers, Quart. J. Math. Oxford 69 (2018), 377- 389. [44] M.F. Teixeira and D.E. Edmunds, Interpolation theory and measures of non-compactness, Math. Nachr. 104 (1981), 129-135. [45] H. Triebel, Interpolation Theory, Function Spaces, Di�erential Operators, North-Holland, Amsterdam, 1978. [46] H. Triebel, Theory of Function Spaces II, Birkh�auser, Basel, 1992.https://hdl.handle.net/20.500.14352/6504We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with [θ] = 0; 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces.engjournal articleopen access517Logarithmic interpolation methodsmeasure of non-compactnesscompact operatorsLorentz-Zygmund spacesEspacios de Lorentz-ZygmundMatemáticas (Matemáticas)Análisis matemático12 Matemáticas1202 Análisis y Análisis Funcional