Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized shifts through derivations' concept in $\ell^p(\tau)$ spaces   In the following text for $p\in[1,\infty]$, nonzero cardinal number $\tau$,
self--map $\varphi:\tau\to\tau$ if there exists $N\in\mathbb{N}$ such that
$\varphi^{-1}(\alpha)$ has at most $N$ elements for each $\alpha<\tau$, and
operators $\psi,\lambda:\ell^p\tau)\to\ell^p(\tau)$ we prove the generalized
shift
$\mathop{\sigma_\varphi\restriction_{\ell^p(\tau)}:\ell^p(\tau)\to\ell^p(\tau)\:\:\:\:\:\:\:\:\:}\limits_{\:\:\:\:\:\:\:\:\:
(x_\alpha)_{\alpha<\tau}\mapsto (x_{\varphi(\alpha)})_{\alpha<\tau}}$:
  $\bullet$ is a $(\psi,\lambda)-$derivation if and only if there exists
$\mathsf{r}\in{\mathbb C}^\tau$ with $\psi={\mathsf
r}\sigma_\varphi\restriction_{\ell^p(\tau)}$ and
$\lambda=((1)_{\alpha<\tau}-{\mathsf
r})\sigma_\varphi\restriction_{\ell^p(\tau)}$,
  $\bullet$ is a $\psi-$derivation if and only if
$\psi=\frac12\sigma_\varphi\restriction_{\ell^p(\tau)}$,
  $\bullet$ is not a (Jordan, Jordan triple) derivation,
  $\bullet$ is a generalized (Jordan, Jordan triple) derivation if and only if
$\varphi=id_\tau$.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
7
The categories of this paper are: hep-th