Vol. 105, No. 2, 1983

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Norm attaining operators on some classical Banach spaces

Walter Schachermayer

Vol. 105 (1983), No. 2, 427–438
Abstract

We construct an operator from L1[0,1] to C[0,1] which may not be approximated by norm attaining operators with respect to the operator norm. This solves a question raised by J. Johnson and J. Wolfe and furnishes the first example of a pair of classical Banach spaces such that the norm attaining operators are not dense. C[0,1] is the first example of a classical Banach space which does not have property B.

On the other hand, we show that a weakly compact operator from C(K) into a Banach space X may be approximated in norm by norm attaining operators. This shows in particular that the norm attaining operators are dense in B(C(K),L1[0,1]) and B(C(K),l2), thus solving two questions raised by Johnson and Wolfe.

Mathematical Subject Classification 2000
Primary: 46B25
Secondary: 47B99
Milestones
Received: 1 July 1981
Published: 1 April 1983
Authors
Walter Schachermayer