Document Type
Article
Publication Date
1998
Digital Object Identifier (DOI)
https://doi.org/10.1155/S1085337598000542
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.
Rights Information
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Yes
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. 37.
https://digitalcommons.usf.edu/mth_facpub/37
