Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral algebraic curves and decomposable operator tuples   Joint spectra of tuples of operators are subsets in complex projective space.
The corresponding tuple of operators can be viewed as an infinite dimensional
analog of a determinantal representation of the joint spectrum. We investigate
the relationship between the geometry of the spectrum and the properties of the
operators in the tuple when these operators are self-adjoint. In the case when
the spectrum contains an algebraic curve passing through an isolated spectral
point of one of the operators we give necessary and sufficient geometric
conditions for the operators in the tuple to have a common reducing subspace.
We also address spectral continuity and obtain a norm estimate for the
commutant of a pair of self-adjoint matrices in terms of the Hausdorff distance
of their joint spectrum to a family of lines.

21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int