Abstract. The Fourier algebra A(G) and the Fourier-Stieltjes algebra B(G)
of a locally compact group G were introduced by Eymard [1964]. If G is
abelian, A(G) and B(G) can be identified, via Fourier transform, with L1(̂G^)
and the measure algebra M (̂G^) of the dual group ̂G^, respectively. Cohen
[1960] characterized the homomorphisms from A(H) into B(G) for H and
G locally compact abelian groups using a characterization of idempotents
in B(G). Homomorphisms of Fourier algebras for general locally compact
groups were studied by Ilie-Spronk [2005] and Daws [2022].
We provide necessary and sufficient conditions for the existence of idem-
potents of arbitrarily large norm 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 ex-
istence of homomorphisms of arbitrarily large norm from A(H) into B(G)
for every locally compact group H.
This is a report of joint work with M. Anoussis (Univ. of the Aegean)
and G. K. Eleftherakis (Univ. of Patras).
of a locally compact group G were introduced by Eymard [1964]. If G is
abelian, A(G) and B(G) can be identified, via Fourier transform, with L1(̂G^)
and the measure algebra M (̂G^) of the dual group ̂G^, respectively. Cohen
[1960] characterized the homomorphisms from A(H) into B(G) for H and
G locally compact abelian groups using a characterization of idempotents
in B(G). Homomorphisms of Fourier algebras for general locally compact
groups were studied by Ilie-Spronk [2005] and Daws [2022].
We provide necessary and sufficient conditions for the existence of idem-
potents of arbitrarily large norm 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 ex-
istence of homomorphisms of arbitrarily large norm from A(H) into B(G)
for every locally compact group H.
This is a report of joint work with M. Anoussis (Univ. of the Aegean)
and G. K. Eleftherakis (Univ. of Patras).
Presentation Date:
Friday, April 5, 2024
Location:
Algebras in Analysis, https://alganal.wordpress.com/
