Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounded multiplicative Toeplitz operators on sequence spaces   In this paper, we study the linear mapping which sends the sequence
$x=(x_n)_{n \in \mathbb{N}}$ to $y=(y_n)_{n \in \mathbb{N}}$ where $y_n =
\sum_{k=1}^\infty f(n/k)x_k$ for $f: \mathbb{Q}^+ \to \mathbb{C}$. This
operator is the multiplicative analogue of the classical Toeplitz operator, and
as such we denote the mapping by $\mathscr{M}_f$. We show that for $1 \leq p
\leq q \leq \infty$, if $f \in \ell^r(\mathbb{Q}^+)$, then
$\mathscr{M}_f:\ell^p \to \ell^q$ is bounded where $\frac{1}{r} = 1 -
\frac{1}{p} + \frac{1}{q} $. Moreover, for the cases when $p=1$ with any $q$,
$p=q$, and $q=\infty$ with any $p$, we find that the operator norm is given by
$\|\mathscr{M}_f\|_{p,q} = \|f\|_{r,\mathbb{Q}^+}$ when $f \geq 0$. Finding a
necessary condition and the operator norm for the remaining cases highlights an
interesting connection between the operator norm of $\mathscr{M}_f$ and
elements in $\ell^p$ that have a multiplicative structure, when considering
$f:\mathbb{N} \to \mathbb{C}$. We also provide an argument suggesting that $f
\in \ell^r$ may not be a necessary condition for boundedness when
$1<p<q<\infty$.

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The categories of this paper are: stat
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat