Measures of non-compactness in Orlicz modular spaces

• Autores: J.B. Baillon, Asuman Güven Aksoy
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 44, Fasc. 1-3, 1993, págs. 1-12
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper we show that the ball measure of non-compactness of a norm bounded subset of an Orlicz modular space $L^\psi$ is equal to the limit of its $n$-widths. We also obtain several inequalities between the measures of noncompactness and the limit of the $n$-widths for modular bounded subsets of $L^\psi$ which do not have $\Delta_2$-condition. Minimum conditions on $\psi$ to have such results are specified and an example of such a function $\psi$ is provided.

• Referencias bibliográficas
  • A.G. Aksoy, The radius of the essential spectrum, J. Math. Anal. and Appl. Vol. 128, No. 1 (1987), 101–107.
  • J. Banaś and K. Goebel, Measures of noncompactness in Banach spaces, Notes in Pure and Applied Math., Marcel Dekker, Vol. 60 (1980), New York.
  • G. Drabo, Punti uniti in transformazioni a condominio non compatto, Rend. Sem. Mat. Univ. Padua 24 (1955), 84–92.
  • D.E. Edmunds, Embeddings of Sobolev spaces, Proceedings of spring school in non-linear analysis, function spaces, and applications, Teubner-Texte...
  • D.E. Edmunds and R.M. Edmunds, Entropy and approximation numbers of embeddings in Orlicz spaces, J. London Math. Soc. (2), 32, No. 3, (1985),...
  • D.E. Edmunds and W\.D. Evans, Spectral Theory and Differential Operators, Oxford Science Publications, Clarendon Press, Oxford, (1987).
  • M.A. Khamsi, W.M. Kozlowski and S. Reich, Fixed point theory in modular function spaces, Journal of non-linear analysis, 14 (1990), 935–953.
  • W.M. Kozlowski, Modular function spaces, Marcel Dekker, New York and Basel, 1988.
  • M.A. Krasnoselskii and Ya.B. Rutickii, Convex functions and Orlicz spaces, (translation), P. Noordhoff Ltd., Groningen, 1961.
  • A. Lebow and M. Schechter, Semigroup of operators and measures of non-compactness, J. Func. Anal. 7 (1971), 1–26.
  • J. Lindenstrauss and J. Tzafriri, Classical Banach spaces II, Springer-Verlag, Berlin-Heidelberg-New York, 1979.
  • J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, Vol. 1034, Springer-Verlag, Berlin, 1983.
  • R.D. Nussbaum, The radius of the essential spectrum, Duke Math. J. 37 (1970), 473–479.
  • M.M. Rao and Z.D. Ren, Theory of Orlicz Spaces, Marcel Dekker, Inc., New York, 1991.
  • S. Reich (1973), Fixed points of condensing functions, J. Math. Anal. and Appl. 41 (1973), 460–467.
  • S. Reich, Fixed points in locally convex spaces, Math. Z. 125 (1972), 17–31.
  • B.N. Sadovskii, Limit-compact and condensing operators, Russian Math. Surveys 27 (1972), 85–155.