Abstract
AbstractLetAp(G) be the Figa-Talamanca, Herz Banach Algebra onG; thusA2(G) is the Fourier algebra. Strong Ditkin (SD) and Extremely Strong Ditkin (ESD) sets for the Banach algebrasApr(G) are investigated for abelian and nonabelian locally compact groupsG. It is shown that SD and ESD sets forAp(G) remain SD and ESD sets forApr(G), with strict inclusion for ESD sets. The case for the strict inclusion of SD sets is left open.A result on the weak sequential completeness ofA2(F) for ESD setsFis proved and used to show that Varopoulos, Helson, and Sidon sets are not ESD sets forA2r(G), yet they are such forA2(G) for discrete groupsG, for any 1 ≤r≤ 2.A result is given on the equivalence of the sequential and the net definitions of SD or ESD sets forσ-compact groups.The above results are new even ifGis abelian.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
