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Best possible Compactness Results of Lions-Peetre Type


Cobos, Fernando y Cwikel, M. y Matos, P. (2001) Best possible Compactness Results of Lions-Peetre Type. Proceedings of the Edinburgh Mathematical Society, 44 (Part 1). pp. 153-173. ISSN 0013-0915

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If T : A0 ! B boundedly and T : A1 ! B compactly, then a result of Lions{Peetre shows that T : A ! B compactly for a certain class of spaces A which are intermediate with respect to A0 and A1. We investigate to what extent such results can hold for arbitrary intermediate spaces A. The `dual' case of an operator S such that S : X ! Y0 boundedly and S : X ! Y1 compactly, is also considered,
as well as similar questions for other closed operator ideals.

Tipo de documento:Artículo
Palabras clave:Interpolation of Compact Operators; Rank-One Interpolation Spaces;General Intermediate Spaces; Operator Ideals; Mathematics
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:15165

C. Bennett and R. Sharpley, Interpolation of operators (Academic Press, New York,


J. Bergh and J. L¨ofstr¨om, Interpolation spaces. An introduction, Grundlehren der

Mathematische Wissenschaften, vol. 223 (Springer, Berlin, 1976).

O. J. Beucher, On interpolation of strictly (co-)singular linear operators, Proc. R. Soc.

Edinb. A112 (1989), 263{269.

Y. Brudnyi and N. Krugljak, Interpolation functors and interpolation spaces, vol. 1

(North Holland, Amsterdam, 1991).

F. Cobos, T. K¨uhn and T. Schonbek, One-sided compactness results for Aronszajn{

Gagliardo functors, J. Funct. Analysis 106 (1992), 274{313.

F. Cobos, A. Manzano and A. Mart_inez, Interpolation theory and measures related

to operator ideals, Q. J. Math. Oxford (2) 50 (1999), 401{416.

F. Cobos and J. Peetre, Interpolation of compactness using Aronszajn{Gagliardo functors,

Israel J. Math. 68 (1989), 220{240.

J. Diestel, H. Jarchow and A. Tonge, Absolutely summing operators, Cambridge

Studies in Advanced Mathematics, vol. 43 (Cambridge University Press, 1995).

A. A. Dmitriev, The interpolation of one-dimensional operators, Vorone_z Gos. Univ.

Trudy Nau_cn.-Issled. Inst. Mat. VGU Vyp. 11 Sb. Statej Funkcional. Anal. i Prilozen 11

(1973), 31{43 (in Russian).

E. Gagliardo, A uni_ed structure in various families of function spaces. Compactness

and closure theorems, in Proc. Int. Symp. Linear Spaces, Jerusalem 1960, pp. 237{241

(Pergamon, Oxford, 1961).

G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals (I), Math.

Z. 27 (1928), 565{606.

S. Heinrich, Closed operator ideals and interpolation, J. Funct. Analysis 35 (1980),


M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik and P. E. Sobolevskii,

Integral operators in spaces of summable functions (Noordho_, Leyden, 1976).

J. L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Etudes

Sci. Publ. Math. 19 (1964), 5{68.

M. Masty lo, On interpolation of compact operators, Funct. Approx. Comment. Math.

26 (1998), 293{311.

A. Persson, Compact linear mappings between interpolation spaces, Ark. Mat. 5 (1964),


A. Pietsch, Operator ideals (North-Holland, Amsterdam, 1980).

E. I. Pustylnik, On optimal interpolation and some interpolation properties of Orlicz

spaces, Soviet. Math. Dokl. 27 (1983), 333{336. (Translation from Dokl. Akad. Nauk SSSR

269 (1983), 292{295.)

E. I. Pustylnik, Embedding functions and their role in interpolation theory, Abstract

Appl. Analysis 1 (1996), 305{325.

M. F. Teixeira and D. E. Edmunds, Interpolation theory and measures of non-compactness,

Math. Nachr. 104 (1981), 129{135.

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Última Modificación:06 Feb 2014 10:17

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