Applications of Kazhdan's property (T) to automatic continuity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:307

Article

Alaminos, J ; Extremera, J ; Villena, AR

关键词: automatic continuity;    Kazhdan's property;    strong Kazhdan's property;    unitary representations;    operators commuting with translations;    translation invariant linear functionals;   

DOI  :  10.1016/j.jmaa.2004.11.066

来源: Elsevier

【 摘 要 】

Let G be a compact group which has the strong Kazhdan's property (T) and let iota be an isometric representation of G on L-P (mu) for some measure space (Omega, Sigma, mu) and 1 < p < infinity. We characterize the continuity of all the linear operators from L P (it) which commute with translations and the property of parallel to (.) parallel to(p) being the unique norm (up to equivalence) on L-P(mu) with respect to which all translations are continuous in terms of the finite-dimensionality of the subspace of all invariant functions. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free