Open Access
1998 Spectral properties of operators that characterize $\ell^{(n)}_\infty$
B. L. Chalmers, B. Shekhtman
Abstr. Appl. Anal. 3(3-4): 237-246 (1998). DOI: 10.1155/S1085337598000542


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.


Download Citation

B. L. Chalmers. B. Shekhtman. "Spectral properties of operators that characterize $\ell^{(n)}_\infty$." Abstr. Appl. Anal. 3 (3-4) 237 - 246, 1998.


Published: 1998
First available in Project Euclid: 8 April 2003

zbMATH: 0983.46010
MathSciNet: MR1749410
Digital Object Identifier: 10.1155/S1085337598000542

Primary: 46B20
Secondary: 51M20

Rights: Copyright © 1998 Hindawi

Vol.3 • No. 3-4 • 1998
Back to Top