Abstract and Applied Analysis
Volume 3 (1998), Issue 3-4, Pages 237-246

Spectral properties of operators that characterize (n)

B. L. Chalmers1 and B. Shekhtman2

1Department of Mathematics, University of California, Riverside 92521, California, USA
2Department of Mathematics, University of South Florida, Tampa 33620-5700, Florida, USA

Received 8 October 1998

Copyright © 1998 B. L. Chalmers and B. Shekhtman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that the identity is an operator with the following property: if the operator, initially defined on an n-dimensional Banach space V, can be extended to any Banach space with norm 1, then V is isometric to (n). We show that the set of all such operators consists precisely of those with spectrum lying in the unit circle. This result answers a question raised in [5] for complex spaces.