Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal elements for non-linear operators and their applications   We prove that under certain topological conditions on the set of universal
elements of a continuous map $T$ acting on a topological space $X$, that the
direct sum $T\oplus M_g$ is universal, where $M_g$ is multiplication by a
generating element of a compact topological group. We use this result to
characterize $\R_+$-supercyclic operators and to show that whenever $T$ is a
supercyclic operator and $z_1,...,z_n$ are pairwise different non-zero complex
numbers, then the operator $z_1T\oplus {...}\oplus z_n T$ is cyclic. The latter
answers affirmatively a question of Bayart and Matheron.

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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg