Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some sufficient conditions for existence of hyperinvariant subspaces for
  operators intertwined with unitaries   For a power bounded or polynomially bounded operator $T$ sufficient
conditions for the existence of a nontrivial hyperinvariant subspace are given.
The obtained hyperinvariant subspaces of $T$ have the form of the closure of
the range of $\varphi(T)$. Here $\varphi$ is a singular inner function, if $T$
is polynomially bounded, or $\varphi$ is an analytic in the unit disc function
with absolutely summable Taylor coefficients and singular inner part, if $T$ is
supposed to be power bounded only.
  Also, an example of a quasianalytic contraction $T$ is given. The
quasianalytic spectral set of $T$ is not the whole unit circle $\mathbb T$,
while $\sigma(T)=\mathbb T$. Proofs are based on results by Esterle, Kellay,
Borichev and Volberg.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn