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Indices defined by Interpolation Scales and Applications

Fernández-Cabrera, Luz M. and Cobos, Fernando and Hernández, Francisco L. and Sánchez, Víctor M. (2004) Indices defined by Interpolation Scales and Applications. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 134 (Part 4). pp. 695-717. ISSN 0308-2105

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Abstract

We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.


Item Type:Article
Uncontrolled Keywords:Rearrangement-Invariant Spaces; Strictly-Singular Inclusions; Operator Ideals; Embeddings; Mathematics, Applied; Mathematics
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:15126
References:

S. V. Astashkin. Disjointly strictly singular inclusions of symmetric spaces. Math. Notes

65 (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 717

A. 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 between

Banach 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 to

operator ideals. Q. J. Math. 50 (1999), 401–416.

F. Cobos, A. Manzano, A. Mart´ınez and P. Matos. On interpolation of strictly singular

operators, 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. Indiana

Univ. 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 and

interpolation. 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 strictlysingular

inclusions 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 inclusions

between rearrangement invariant spaces. Studia Math. 144 (2001), 209–226.

F. L. Hern´andez, S. Ya. Novikov and E. M. Semenov. Strictly singular embeddings between

rearrangement 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. Studia

Math. 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).

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