Complutense University Library

On a result of Peetre about interpolation of operator spaces

Cobos, Fernando and Signes, Teresa (2000) On a result of Peetre about interpolation of operator spaces. Publicacions Matemàtiques , 44 (2). pp. 457-481. ISSN 0214-1493

[img] PDF
Restricted to Repository staff only until 2020.

232kB

Official URL: http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/37997/40343

View download statistics for this eprint

==>>> Export to other formats

Abstract

We establish interpolation formulae for operator spaces that are components of a given quasi-normed operator ideal.

Item Type:Article
Uncontrolled Keywords:Real interpolation; quasi-normed operator ideals; tensor product; regularity; linearizability; injectivity; surjectivity; inclusion relations
Subjects:Sciences > Mathematics > Numerical analysis
ID Code:15209
References:

J. Bergh and J. Löfström, “Interpolation spaces. An introduction”, Grundlehren der Mathematischen Wissenschaften 223, Springer-Verlag, Berlin, 1976. 480 F. Cobos, T. Signes Mathematischen Wissenschaften 223, Springer-Verlag, Berlin, 1976. 480 F. Cobos, T. Signes

F. Cobos, M. Cwikel and P. Matos, Best possible compactness result of Lions-Peetre type, Proc. Edinburgh Math. Soc. (2) (to appear).

F. Cobos, A. Manzano and A. Martínez, Interpolation theory and measures related to operator ideals, Quart. J. Math. Oxford Ser. (2) 50(200) (1999), 401–416.

J. Diestel, H. Jarchow and A. Tonge, “Absolutely summing operators”, Cambridge Studies in Advanced Mathematics 43, Cambridge University Press, Cambridge, 1995.

A. A. Dmitriev, The interpolation of one-dimensional operators, Voroneˇz. Gos. Univ. Trudy Nauˇcn.-Issled. Inst. Mat. VGU (Vyp. 11 Sb. Statei Funkcional. Anal. i Prilozen.) 11 (1973), 31–43, (Russian).

W. F. Donoghue, The interpolation of quadratic norms, Acta Math. 118 (1967), 251–270.

D. E. Edmunds and D. D. Haroske, Embeddings in spaces of Lipschitz type, entropy and approximation numbers, and applications, J. Approx. Theory 104(2) (2000), 226–271.

D. E. Edmunds and H. Triebel, “Function spaces, entropy numbers, differential operators”, Cambridge Tracts in Mathematics 120, Cambridge University Press, Cambridge, 1996.

D. J. H. Garling and S. J. Montgomery-Smith, Complemented subspaces of spaces obtained by interpolation, J. London Math. Soc. (2) 44(3) (1991), 503–513.

J. Gustavsson and J. Peetre, Interpolation of Orlicz spaces, Studia Math. 60(1) (1977), 33–59.

O. Kouba, On the interpolation of injective or projective tensor products of Banach spaces, J. Funct. Anal. 96(1) (1991), 38–61.

P. Nilsson, Reiteration theorems for real interpolation and approximation spaces, Ann. Mat. Pura Appl. (4) 132 (1982), 291–330.

V. I. Ovchinnikov, Interpolation in symmetrically normed ideals of operators that act in different spaces, Funktsional. Anal. i Prilozhen. 28(3) (1994), 80–82; translation in Funct. Anal. Appl. 28(3) (1994), 213–215.

V. I. Ovchinnikov, Lions-Peetre construction for couples of operator spaces, Russian J. Math. Phys. 3(3) (1995), 407–410.

J. Peetre, A theory of interpolation of normed spaces, Notas de Matem´atica 39, Instituto de Matem´atica Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1968.

J. Peetre, Zur Interpolation von Operatorenr¨aumen, Arch. Math. (Basel) 21 (1970/71), 601–608. On A Result of Peetre 481

J. Peetre, On the connection between the theory of interpolation spaces and approximation theory, in “Proceedings of the Conference on the Constructive Theory of Functions (Approximation Theory)” (Budapest, 1969), Akad´emiai Kiad´o, Budapest, 1972, pp. 351–363.

A. Pietsch, “Operator ideals”, North-Holland Mathematical Library 20, North-Holland Publishing Co., Amsterdam, 1980.

A. Pietsch, “Eigenvalues and s-numbers”, Cambridge Studies in Advanced Mathematics 13, Cambridge University Press, Cambridge, 1987.

E. Pustylnik, Embedding functions and their role in interpolation theory, Abstr. Appl. Anal. 1(3) (1996), 305–325.

H. Triebel, “Interpolation theory, function spaces, differential operators”, North-Holland Mathematical Library 18, North-Holland Publishing Co., Amsterdam, 1978.

Deposited On:16 May 2012 09:18
Last Modified:06 Feb 2014 10:18

Repository Staff Only: item control page