Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Translation-invariant linear forms on $ L\sb p(G)$


Author: Joseph Rosenblatt
Journal: Proc. Amer. Math. Soc. 94 (1985), 226-228
MSC: Primary 43A15
DOI: https://doi.org/10.1090/S0002-9939-1985-0784168-5
MathSciNet review: 784168
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a compact group such that the identity representation of $ G$ is not contained in the regular representation on $ L_2^0(G,{\lambda _G})$ of $ G$ with the discrete topology. Then any left translation invariant linear form on $ {L_p}(G),1 < p < \infty $, is continuous and must be a constant times the Haar integral. This shows that many classical matrix groups $ G$ admit only continuous left translation invariant linear forms on $ {L_p}(G),1 < p < \infty $.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A15

Retrieve articles in all journals with MSC: 43A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0784168-5
Article copyright: © Copyright 1985 American Mathematical Society