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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  for complex spaces.
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Citation / Publisher Attribution
Abstract and Applied Analysis, v. 3, art. 490425
Scholar Commons Citation
Chalmers, B. L. and Shekhtman, B., "Spectral Properties of Operators that Characterize ℓ∞(n)" (1998). Mathematics and Statistics Faculty Publications. 70.