Spectral properties of operators that characterize ℓ ∞ ( n )

B. L. Chalmers and B. Shekhtman

Abstract and Applied Analysis, 1998, vol. 3, 1-10

Abstract:

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 ℓ ∞ ( 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.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:490425

DOI: 10.1155/S1085337598000542

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