Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homological Properties of the Algebra of Compact Operators on a Banach
  Space   The conditions on a Banach space, $E$, under which the algebra,
$\mathcal{K}(E)$, of compact operators on $E$ is right flat or homologically
unital are investigated. These homological properties are related to
factorization in the algebra and it is shown that, for $\mathcal{K}(E)$, they
are closely associated with the approximation property for $E$. The class of
spaces, $E$, such that $\mathcal{K}(E)$ is known to be right flat and
homologically unital is extended to include spaces which do not have the
bounded compact approximation property.

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The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph