Spectral properties of operators that characterize ℓ∞(n)

B. L. Chalmers and B. Shekhtman

Abstract and Applied Analysis, 1998, vol. 3, issue 3-4, 237-246

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:wly:jnlaaa:v:3:y:1998:i:3-4:p:237-246

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