Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A local spectral condition for strong compactness with some applications
  to bilateral weighted shifts   An algebra of bounded linear operators on a Banach space is said to be {\em
strongly compact} if its unit ball is precompact in the strong operator
topology, and a bounded linear operator on a Banach space is said to be {\em
strongly compact} if the algebra with identity generated by the operator is
strongly compact. Our interest in this notion stems from the work of Lomonosov
on the existence of invariant subspaces. We provide a local spectral condition
that is sufficient for a bounded linear operator on a Banach space to be
strongly compact. This condition is then applied to describe a large class of
strongly compact, injective bilateral weighted shifts on Hilbert spaces,
extending earlier work of Fern\'andez-Valles and the first author. Further
applications are also derived, for instance, a strongly compact, invertible
bilateral weighted shift is constructed in such a way that its inverse fails to
be a strongly compact operator.

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The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
29
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: solv-int