Ir al contenido

Documat


Generalized Lions-Peetre methods of constants and means and operator ideals

  • Autores: Antonio Manzano Rodríguez Árbol académico, Mieczyslaw Mastylo Árbol académico
  • Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 58, Fasc. 1, 2007, págs. 45-60
  • Idioma: inglés
  • Enlaces
  • Resumen
    • We establish results on interpolation of Rosenthal operators, BanachSaks operators, Asplund operators and weakly compact operators by means of generalized LionsPeetre methods of constants and means. Applications are presented for the Kmethod space generated by the Calder¿onLozanovskii space parameters

  • Referencias bibliográficas
    • B. Beauzamy, Espaces d’Interpolation Réels: Topologie et Géométrie, Lecture Notes in Mathematics 666, Springer, Berlin, 1978.
    • J. Bergh and J. Löfström, Interpolation Spaces, An Introduction, Grundlehren der Mathematischen Wissenschaften 223, Springer-Verlag, Berlin-New...
    • R.D. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodým Property, Lecture Notes in Mathematics 993, Springer-Verlag, Berlin,...
    • Yu.A. Brudnyi and N.Ya. Krugljak, Interpolation Functors and Interpolation Spaces, I, North-Holland Publishing Co., Amsterdam, 1991.
    • F. Cobos, M. Cwikel, and P. Matos, Best possible compactness results of Lions-Peetre type, Proc. Edinb. Math. Soc. (2) 44 (2001), 153–172.
    • F. Cobos, L.M. Fernández-Cabrera, A. Manzano, and A. Martínez, Real interpolation and closed operator ideals, J. Math. Pures Appl. (9) 83...
    • F. Cobos, L.M. Fernández-Cabrera, A. Manzano, and A. Martínez, On interpolation of Asplund operators, Math. Z. 250 (2005), 267–277.
    • F. Cobos, A. Manzano, A. Martínez, and P. Matos, On interpolation of strictly singular operators, strictly co-singular operators and related...
    • F. Cobos and A. Martínez, Extreme estimates for interpolated operators by the real method, J. London Math. Soc. (2) 60 (1999), 860–870.
    • W\.J. Davis, T. Figiel, W\.B. Johnson, and A. Pelczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311–327.
    • V.I. Dmitriev, S.G. Krein, and V.I. Ovchinnikov, Fundamentals of the theory of interpolation of linear operators, In: Geometry of Linear Spaces...
    • P. Erdös and M. Majidor, A note on regular methods of summability and the Banach-Saks property, Proc. Amer. Math. Soc. 59 (1976), 232–234.
    • M. Fan, Interpolation methods of constants and means with quasi-power function parameters, Math. Scand. 88 (2001), 79–95.
    • D.J.H. Garling and S.J. Montgomery-Smith, Complemented subspaces of spaces obtained by interpolation, J. London Math. Soc. (2) 44 (1991),...
    • S. Heinrich, Closed operator ideals and interpolation, J. Funct. Anal. 35 (1980), 397–411.
    • S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981), 50–73.
    • S.G. Kreĭn, Ju.I. Petunin, and E.M. Semenov, Interpolation of Linear Operators, American Mathematical Society, Providence, R.I., 1982.
    • A. Kryczka, S. Prus, and M. Szczepanik, Measure of weak noncompactness and real interpolation of operators, Bull. Austral. Math. Soc. 62 (2000),...
    • J.L. Lions and J. Peetre, Sur une class d’espaces d’interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5–68.
    • G.Ya. Lozanovskiĭ, On some Banach lattices IV, Sibirsk. Mat. Z. 14 (1973), 140–155 (in Russian); English transl.: Siberian. Math. J. 14 (1973),...
    • M. Mastyło, Interpolation spaces containing $\ell^1$, J. Math. Pures Appl. (9) 68 (1989), 153–162.
    • M. Mastyło, On interpolation of weakly compact operators, Hokkaido Math. J. 22 (1993), 105–114.
    • M. Mastyło, Interpolation methods of means and orbits, Studia Math. 171 (2005), 153–175.
    • M. Mastyło, Interpolation Banach lattices containing no isomorphic copies of $c\_0$, (Preprint).
    • A. Pietsch, Operator Ideals, North-Holland Publishing Co., Amsterdam-New York, 1980.
    • W. Schachermayer, The Banach-Saks property is not $L^2$-hereditary, Israel J. Math. 40 (1981), 340–344.
    • C. Stegall, The Radon-Nikodým property in conjugate Banach spaces, II, Trans. Amer. Math. Soc. 264 (1981), 507–519.
    • A.C. Zaanen, Riesz Spaces, II, North-Holland Publishing Co., Amsterdam, 1983.

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno