Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian, amenable operator algebras are similar to C*-algebras   Suppose that H is a complex Hilbert space and that B(H) denotes the bounded
linear operators on H. We show that every abelian, amenable operator algebra is
similar to a C*-algebra. We do this by showing that if A is an abelian
subalgebra of B(H) with the property that given any bounded representation
$\varrho: A \to B(H_\varrho)$ of A on a Hilbert space $H_\varrho$, every
invariant subspace of $\varrho(A)$ is topologically complemented by another
invariant subspace of $\varrho(A)$, then A is similar to an abelian
$C^*$-algebra.

29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn