Cobos, FernandoFernández-Cabrera, Luz M.Martínez, Antón2023-06-182023-06-182016[1] A.G. Aksoy, H.-O. Tylli, Interpolation of the essential spectrum and the essential norm, Banach Center Publ. 68 (2005) 9–18. [2] E. Albrecht, Spectral Interpolation, Oper. Theory Adv. Appl., vol. 14, Birkhäuser, Basel, 1984, pp. 13–37. [3] C. Bennet, R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988. [4] J. Bergh, J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976. [5] Yu.A. Brudny˘ı, N.Ya. Krugljak, Interpolation Functors and Interpolation Spaces, vol. 1, North-Holland, Amsterdam, 1991. [6] B. Carl, I. Stephani, Entropy, Compactness and the Approximation of Operators, Cambridge Univ. Press, cambridge, 1990. [7] F. Cobos, O. Domínguez, On Besov spaces of logarithmic smoothness and Lipschitz spaces, J. Math. Anal. Appl. 425 (2015) 71–84. [8] F. Cobos, L.M. Fernández-Cabrera, T. Kühn, T. Ullrich, On an extreme class of real interpolation spaces, J. Funct. Anal. 256 (2009) 2321–2366. [9] F. Cobos, L.M. Fernández-Cabrera, A. Martínez, Abstract K and J spaces and measure of non-compactness, Math. Nachr. 280 (2007) 1698–1708. [10] F. Cobos, L.M. Fernández-Cabrera, A. Martínez, Measure of Non-Compactness of Operators Interpolated by Limiting Real Methods, Oper. Theory Adv. Appl., vol. 219, Springer, Basel, 2012, pp. 37–54. [11] F. Cobos, L.M. Fernández-Cabrera, A. Martínez, On a paper of Edmunds and Opic on limiting interpolation of compact operators between Lp spaces, Math. Nachr. 288 (2015) 167–175. [12] F. Cobos, P. Fernández-Martínez, A. Martínez, Interpolation of the measure of non-compactness by the real method, Studia Math. 135 (1999) 25–38. [13] F. Cobos, T. Kühn, Equivalence of K- and J-methods for limiting real interpolation spaces, J. Funct. Anal. 261 (2011) 3696–3722. [14] F. Cobos, A. Segurado, Description of logarithmic interpolation spaces by means of the J-functional and pplications, J. Funct. Anal. 268 (2015) 2906–2945. [15] J.M. Cordeiro, Interpolación de ciertas clases de operadores por métodos multidimensionales, Publicaciones do Depto. Matemática Aplicada I, Sec. 1, n. 9, Universidade de Vigo, 1999. [16] D.E. Edmunds, W.D. Evans, Spectral Theory and Differential Operators, Clarendon Press, Oxford, 1987. [17] D.E. Edmunds, B. Opic, Limiting variants of Krasnosel’ski˘ı’s compact interpolation theorem, J. Funct. Anal. 266 (2014) 3265–3285. [18] W.D. Evans, B. Opic, Real interpolation with logarithmic functors and reiteration, Canad. J. Math. 52 (2000) 920–960. [19] W.D. Evans, B. Opic, L. Pick, Real interpolation with logarithmic functors, J. Inequal. Appl. 7 (2002) 187–269. [20] J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978) 289–305. [21] S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981) 50–73. [22] H. König, Eigenvalue Distributions of Compact Operators, Birkhäuser, Basel, 1986. [23] R.D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 37 (1970) 473–479. [24] M. Schechter, Principles of Functional Analysis, Amer. Math. Soc., Providence, 2002. [25] R. Szwedek, Measure of non-compactness of operators interpolated by real method, Studia Math. 175 (2006) 157–174. [26] M.F. Teixeira, D.E. Edmunds, Interpolation theory and measure of non-compactness, Math. Nachr. 104 (1981) 129–135. [27] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. [28] M. Zafran, Spectral theory and interpolation of operators, J. Funct. Anal. 36 (1980) 185–204.0022-247Xhttp://10.1016/j.jmaa.2016.01.003https://hdl.handle.net/20.500.14352/24372We study spectral properties of operators on logarithmic perturbations of the real interpolation spaces with θ = 0 or 1. We also establish estimates for the measure of non-compactness of operators interpolated by those methods.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022247X16000135http://www.sciencedirect.com/restricted access517Logarithmic interpolation methodsMeasure of non-compactnessRiesz operatorsEssential spectral radiusAnálisis matemático1202 Análisis y Análisis Funcional