Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diameter two properties in some vector-valued function spaces   We introduce a vector-valued version of a uniform algebra, called the
vector-valued function space over a uniform algebra. The diameter two
properties of the vector-valued function space over a uniform algebra on an
infinite compact Hausdorff space are investigated. Every nonempty relatively
weakly open subset of the unit ball of a vector-valued function space $A(K, (X,
\tau))$ over an infinite dimensional uniform algebra has the diameter two,
where $\tau$ is a locally convex Hausdorff topology on a Banach space $X$
compatible to a dual pair. Under the assumption on $X$ being uniformly convex
with norm topology $\tau$ and the additional condition that $A\otimes X\subset
A(K, X)$, it is shown that Daugavet points and $\Delta$-points on $A(K, X)$
over a uniform algebra $A$ are the same, and they are characterized by the
norm-attainment at a limit point of the Shilov boundary of $A$. In addition, a
sufficient condition for the convex diametral local diameter two property of
$A(K,X)$ is also provided. As a result, the similar results also hold for an
infinite dimensional uniform algebra.

8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int