Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation and Spectral Discontinuity in Banach Algebras   We extend an example of B. Aupetit, which illustrates spectral discontinuity
for operators on an infinite dimensional separable Hilbert space, to a general
spectral discontinuity result in abstract Banach algebras. This can then be
used to show that given any Banach algebra, $Y$, one may adjoin to $Y$ a
non-commutative inessential ideal, $I$, so that in the resulting algebra, $A$,
the following holds: To each $x\in Y$ whose spectrum separates the plane there
corresponds a perturbation of $x$, of the form $z=x+a$ where $a\in I$, such
that the spectrum function on $A$ is discontinuous at $z$.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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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: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys