Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the non-hypercyclicity of scalar type spectral operators and
  collections of their exponentials   Generalizing the case of a normal operator in a complex Hilbert space, we
give a straightforward proof of the non-hypercyclicity of a (bounded or
unbounded) scalar type spectral operator $A$ in a complex Banach space as well
as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of the exponentials of
such an operator, which, under a certain condition on the spectrum of the
operator $A$, coincides with the $C_0$-semigroup generated by $A$. The spectrum
of $A$ lying on the imaginary axis, we also show that non-hypercyclic is the
strongly continuous group $\left\{e^{tA}\right\}_{t\in {\mathbb R}}$ of bounded
linear operators generated by $A$. From the general results, we infer that, in
the complex Hilbert space $L_2({\mathbb R})$, the anti-self-adjoint
differentiation operator $A:=\dfrac{d}{dx}$ with the domain
$D(A):=W_2^1({\mathbb R})$ is non-hypercyclic and so is the left-translation
strongly continuous unitary operator group generated by $A$.

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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
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The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs