Affordable Access

The space of all bounded operators on Hilbert space does not have the approximation property

Authors
Publication Date
Disciplines
  • Law

Abstract

The space of all bounded operators on Hilbert space does not have the approximation property Séminaire d’analyse fonctionnelle École Polytechnique A. SZANKOWSKI The space of all bounded operators onHilbert space does not have the approximation property Séminaire d’analyse fonctionnelle (Polytechnique) (1978-1979), exp. no 14 et 15, p. A 1- A 21+1-7. <http://www.numdam.org/item?id=SAF_1978-1979____A13_0> © Séminaire d’analyse fonctionnelle (École Polytechnique), 1978-1979, tous droits réservés. L’accès aux archives du séminaire d’analyse fonctionnelle implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation com- merciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ SEMINAIRE D ’ A N A L Y S E F 0 N C T 1 0 N N E L L E 1978-1979 THE SPACE OF ALL BOUNDED OPERATORS ON HILBERT SPACE DOES NOT HAVE THE APPROXIMATION PROPERTY A. SZANKOWSKI (Universite de Copenhague) PCOLE POLYTECHNIQUE CENTRE DE MATHPMATIQUES PLATEAU DE PALAISBAU · 91128 PALAISEAU CEDEX · Poste N8 Tilex : ECOLEX 691596 F Expos6s No XIV-XV 12-19 Janvier 1979 XIV-XV.1 A Banach space X is said to have the approximation property if the identity operator on X can be approximated uniformly on every compact subset of X by finite rank operators. We prove the result stated in the title of this talk (or, rather, present the main ideas leading t,o the proof). 1. INTRODUCTION Grothendieck discovered [2] that a Banach space X does not A have the approximation property if and only if there exists QÉ X QX such that where, for we set (We regard, as usual, a PX 0X as a functional on L(X,X) = the space of bounded linear operators from X into X where, for T E IJ(X,X), Enflo solved the approximation problem El

There are no comments yet on this publication. Be the first to share your thoughts.