1. CJM 2015 (vol 67 pp. 827)
 Kaniuth, Eberhard

The BochnerSchoenbergEberlein Property and Spectral Synthesis for Certain Banach Algebra Products
Associated with two commutative Banach algebras $A$ and $B$ and
a character $\theta$ of $B$ is a certain Banach algebra product
$A\times_\theta B$, which is a splitting extension of $B$ by
$A$. We investigate two topics for the algebra $A\times_\theta
B$ in relation to the corresponding ones of $A$ and $B$. The
first one is the BochnerSchoenbergEberlein property and the
algebra of BochnerSchoenbergEberlein functions on the spectrum,
whereas the second one concerns the wide range of spectral synthesis
problems for $A\times_\theta B$.
Keywords:commutative Banach algebra, splitting extension, Gelfand spectrum, set of synthesis, weak spectral set, multiplier algebra, BSEalgebra, BSEfunction Categories:46J10, 46J25, 43A30, 43A45 

2. CJM 2010 (vol 63 pp. 123)
 Granirer, Edmond E.

Strong and Extremely Strong Ditkin sets for the Banach Algebras $A_p^r(G)=A_p\cap L^r(G)$
Let $A_p(G)$ be the FigaTalamanca,
Herz Banach Algebra on $G$; thus $A_2(G)$
is the Fourier algebra. Strong Ditkin (SD) and
Extremely Strong Ditkin (ESD) sets for the Banach algebras
$A_p^r(G)$ are investigated for abelian and nonabelian
locally compact groups $G$. It is shown that SD and ESD sets
for $A_p(G)$ remain SD and ESD sets for $A_p^r(G)$,
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 of $A_2(F)$
for ESD sets $F$ is proved and used to show that Varopoulos,
Helson, and Sidon sets are not ESD sets for $A_2(G)$, yet they
are such for $A_2^r(G)$ for discrete groups $G$, for
any $1\le r\le 2$.
A result is given on the equivalence of the sequential and the net
definitions of SD or ESD sets for $\sigma$compact groups.
The above results are new even if $G$ is abelian.
Keywords:Fourier algebra, FigaTalamancaHerz algebra, locally compact group, Ditkin sets, Helson sets, Sidon sets, weak sequential completeness Categories:43A15, 43A10, 46J10, 43A45 
