Publication: Estimates for the spectrum on logarithmic interpolation spaces.
Loading...
Full text at PDC
Publication Date
2016
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Exportar
Abstract
We 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.
Description
UCM subjects
Unesco subjects
Keywords
Citation
[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.