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- W2049116631 abstract "Let τ be a representation of a compact group G on a Banach space ( X ,||·||). The question we address is whether X carries a unique invariant norm in the sense that ||·|| is the unique norm on X for which τ is a representation. We characterize the uniqueness of norm in terms of the automatic continuity of the invariant functionals in the case when X is a dual Banach space and τ is a σ(X,X ∗ ) -continuous representation of G on X such that τ ( G ) consists of σ(X,X ∗ ) -continuous operators. We illustrate the usefulness of this characterization by studying the uniqueness of the norm on the spaces L p (Ω) , where Ω is a locally compact Hausdorff space equipped with a positive Radon measure and G acts on Ω as a group of continuous invertible measure-preserving transformations." @default.
- W2049116631 created "2016-06-24" @default.
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- W2049116631 date "2004-10-01" @default.
- W2049116631 modified "2023-09-27" @default.
- W2049116631 title "Invariant functionals and the uniqueness of invariant norms" @default.
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- W2049116631 doi "https://doi.org/10.1016/j.jfa.2003.09.005" @default.
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