Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Order theory and interpolation in operator algebras   We continue our study of operator algebras with and contractive approximate
identities (cais). In earlier papers we have introduced and studied a new
notion of positivity in operator algebras, with an eye to extending certain
C*-algebraic results and theories to more general algebras. Here we continue to
develop this positivity and its associated ordering, proving many foundational
facts. We also give many applications, for example to noncommutative topology,
noncommutative peak sets, lifting problems, peak interpolation, approximate
identities, and to order relations between an operator algebra and the
C*-algebra it generates. In much of this it is not necessary that the algebra
have an approximate identity. Many of our results apply immediately to function
algebras, but we will not take the time to point these out, although most of
these applications seem new.

29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg