Spectral properties of operators that characterize $\ell^{(n)}_\infty$
Chalmers, B. L. ; Shekhtman, B.
Abstr. Appl. Anal., Tome 3 (1998) no. 1-2, p. 237-246 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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 $\ell^{(n)}_\infty$ . 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.
Publié le : 1998-05-14
Classification:  46B20,  51M20 
@article{1049832725,
     author = {Chalmers, B. L. and Shekhtman, B.},
     title = {Spectral properties of operators that characterize $\ell^{(n)}\_\infty$},
     journal = {Abstr. Appl. Anal.},
     volume = {3},
     number = {1-2},
     year = {1998},
     pages = { 237-246},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1049832725}
}

Chalmers, B. L.; Shekhtman, B. Spectral properties of operators that characterize $\ell^{(n)}_\infty$. Abstr. Appl. Anal., Tome 3 (1998) no. 1-2, pp.  237-246. http://gdmltest.u-ga.fr/item/1049832725/