Idempotents of large norm and homomorphisms of Fourier algebras

Autor:	Anoussis, M., Eleftherakis, G. K., Katavolos, A.
Rok vydání:	2021
Předmět:	Mathematics - Functional Analysis Mathematics - Operator Algebras primary: 43A22 secondary: 43A30
Zdroj:	Studia Mathematica, 2022
Druh dokumentu:	Working Paper
DOI:	10.4064/sm220111-20-1
Popis:	We provide necessary and sufficient conditions for the existence of idempotents of arbitrarily large norms in the Fourier algebra A(G) and the Fourier-Stieltjes algebra B(G) of a locally compact group G. We prove that the existence of idempotents of arbitrarily large norm in B(G) implies the existence of homomorphisms of arbitrarily large norm from A(H) into B(G) for every locally compact group H. A partial converse is also obtained: the existence of homomorphisms of arbitrarily large norm from A(H) into B(G) for some amenable locally compact group H implies the existence of idempotents of arbitrarily large norm in B(G). Comment: The proof of Theorem 2.4 (2.6 in the previous version) has been corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.12318 Zobrazit plný text záznamu View this record from Arxiv