RT Journal Article T1 Indices defined by Interpolation Scales and Applications A1 Fernández-Cabrera, Luz M. A1 Cobos, Fernando A1 Hernández, Francisco L. A1 Sánchez, Víctor M. AB We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces. PB Cambridge University Press SN 0308-2105 YR 2004 FD 2004 LK https://hdl.handle.net/20.500.14352/49898 UL https://hdl.handle.net/20.500.14352/49898 LA eng NO S. V. Astashkin. Disjointly strictly singular inclusions of symmetric spaces. Math. Notes65 (1999), 3–14.C. Bennett and K. Rudnick. On Lorentz–Zygmund spaces. Dissertationes Math. 175(1980), 1–72.C. Bennett and R. Sharpley. Interpolation of operators (Academic, 1988).J. Bergh and J. L¨ofstr¨om. Interpolation spaces. An introduction (Springer, 1976).Indices defined by interpolation scales and applications 717A. P. Calder´on. Intermediate spaces and interpolation, the complex method. Studia Math.24 (1964), 113–190.F. Cobos and J. Peetre. Interpolation of compactness using Aronszajn–Gagliardo functors.Israel J. Math. 68 (1989), 220–240.F. Cobos and E. Pustylnik. On strictly singular and strictly cosingular embeddings betweenBanach lattices of functions. Math. Proc. Camb. Phil. Soc. 133 (2002), 183–190.F. Cobos, A. Manzano and A. Mart´ınez. Interpolation theory and measures related tooperator ideals. Q. J. Math. 50 (1999), 401–416.F. Cobos, A. Manzano, A. Mart´ınez and P. Matos. On interpolation of strictly singularoperators, strictly cosingular operators and related operator ideals. Proc. R. Soc. Edinb.A130 (2000), 971–989.F. Cobos, M. Cwikel and P. Matos. Best possible compactness results of Lions–Peetre type.Proc. Edinb. Math. Soc. 44 (2001), 153–172.M. Cwikel. Complex interpolation spaces, a discrete definition and reiteration. IndianaUniv. Math. J. 27 (1978), 1005–1009.L. M. Fern´andez-Cabrera. Inclusion indices of function spaces and applications. Math. Proc.Camb. Phil. Soc. 136 (2004), 665–674.A. Garc´ıa del Amo, F. L. Hern´andez and C. Ruiz. Disjointly strictly singular operators andinterpolation. Proc. R. Soc. Edinb. A126 (1996), 1011–1026.A. Garc´ıa del Amo, F. L. Hern´andez, V. M. S´anchez and E. M. Semenov. Disjointly strictlysingularinclusions between rearrangement invariant spaces. J. Lond. Math. Soc. 62 (2000),239–252.S. Heinrich. Closed operator ideals and interpolation. J. Funct. Analysis 35 (1980), 397–411.F. L. Hern´andez, V. M. S´anchez and E. M. Semenov. Disjoint strict singularity of inclusionsbetween rearrangement invariant spaces. Studia Math. 144 (2001), 209–226.F. L. Hern´andez, S. Ya. Novikov and E. M. Semenov. Strictly singular embeddings betweenrearrangement invariant spaces. Positivity 7 (2003), 119–124.S. Janson. Minimal and maximal methods of interpolation. J. Funct. Analysis 44 (1981),50–73.S. G. Kreˇın, Ju. I. Petunin and E. M. Semenov. Interpolation of linear operators (Providence,RI: American Mathematical Society, 1982).J. Lindenstrauss and L. Tzafriri. Classical Banach spaces, vol. II. Function spaces (Springer,1979).G. Ya. Lozanovskii. On some Banach lattices. Siberian Math. J. 10 (1969), 419–431.L. Maligranda. Indices and interpolation. Dissertationes Math. 234 (1985), 1–54.L. Maligranda. Interpolation between sum and intersection of Banach spaces. J. Approx.Theory 47 (1986), 42–53.V. I. Ovchinnikov. The method of orbits in interpolation theory. Math. Rep. 1 (1984),349–515.A. Pietsch. Operator ideals (Amsterdam: North-Holland, 1980).E. Pustylnik. Estimation of position of intermediate spaces for a Banach couple. StudiaMath. 107 (1993), 137–155.V. M. S´anchez. Singularidad de inclusiones entre espacios invariantes por reordenamiento.PhD thesis, Universidad Complutense de Madrid (2002).H. Triebel. Interpolation theory, function spaces, differential operators (Amsterdam: North-Holland, 1978). NO NATO Collaborative Linkage Grant NO Spanish Ministerio de Ciencia y Tecnología DS Docta Complutense RD 29 abr 2024