Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity and amenability conditions for uniform algebras   We give a survey of the known connections between regularity conditions and
amenability conditions in the setting of uniform algebras. For a uniform
algebra $A$ we consider the set, $A_{lc}$, of functions in $A$ which are
locally constant on a (varying) dense open subset of the character space of
$A$. We show that, for a separable uniform algebra $A$, if $A$ has bounded
relative units at every point of a dense subset of the character space of $A$,
then $A_{lc}$ is dense in $A$. We construct a separable, essential, regular
uniform algebra $A$ on its character space $X$ such that every point of $X$ is
a peak point for $A$, $A$ has bounded relative units at every point of a dense
open subset of $X$ and yet $A$ is not weakly amenable. In particular, this
shows that a continuous derivation from a separable, essential uniform algebra
$A$ to its dual need not annihilate $A_{lc}$.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs