Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pairs of projections and commuting isometries   It is known that the non-zero part of compact defect operators of
Berger-Coburn-Lebow pairs (BCL pairs in short) of isometries are diagonal
operators of the form \[ \begin{bmatrix} I_1 & & & \\ & D & & \\ & & - I_2 & \\
& & & - D \\ \end{bmatrix}, \] where $I_1$ and $I_2$ are the identity operators
and $D$ is a positive contractive diagonal operator. We discuss the question of
constructing an irreducible BCL pair from a diagonal operator of the above
type. The answer to this question is sometimes in the affirmative and sometimes
in the negative. This also answers a part of the question raised by He, Qin,
and Yang. Our explicit constructions of BCL pairs yield concrete examples of
pairs of commuting isometries.

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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ