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1. CJM Online first

Kaniuth, Eberhard
 The Bochner-Schoenberg-Eberlein 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 Bochner-Schoenberg-Eberlein property and the algebra of Bochner-Schoenberg-Eberlein 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, BSE-algebra, BSE-functionCategories:46J10, 46J25, 43A30, 43A45

2. CJM 2004 (vol 56 pp. 344)

Miao, Tianxuan
 Predual of the Multiplier Algebra of $A_p(G)$ and Amenability For a locally compact group $G$ and $1 Keywords:Locally compact groups, amenable groups, multiplier algebra, Herz algebraCategory:43A07 3. CJM 2001 (vol 53 pp. 592) Perera, Francesc  Ideal Structure of Multiplier Algebras of Simple$C^*$-algebras With Real Rank Zero We give a description of the monoid of Murray-von Neumann equivalence classes of projections for multiplier algebras of a wide class of$\sigma$-unital simple$C^\ast$-algebras$A$with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of the multiplier algebra$\mul$, is therefore analyzed. In important cases it is shown that, if$A$has finite scale then the quotient of$\mul$modulo any closed ideal$I$that properly contains$A$has stable rank one. The intricacy of the ideal structure of$\mul$is reflected in the fact that$\mul$can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion. Keywords:$C^\ast\$-algebra, multiplier algebra, real rank zero, stable rank, refinement monoidCategories:46L05, 46L80, 06F05