Generalized shifts through derivations' concept in $\ell^p(τ)$ spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910300031156224 |
|---|---|
| author | Arzanesh, Safoura Shirazi, Fatemah Ayatollah Zadeh Hosseini, Arezoo |
| author_facet | Arzanesh, Safoura Shirazi, Fatemah Ayatollah Zadeh Hosseini, Arezoo |
| contents | In the following text for $p\in[1,\infty]$, nonzero cardinal number $τ$, self--map $φ:τ\toτ$ if there exists $N\in\mathbb{N}$ such that $φ^{-1}(α)$ has at most $N$ elements for each $α<τ$, and operators $ψ,λ:\ell^pτ)\to\ell^p(τ)$ we prove the generalized shift $\mathop{σ_φ\restriction_{\ell^p(τ)}:\ell^p(τ)\to\ell^p(τ)\:\:\:\:\:\:\:\:\:}\limits_{\:\:\:\:\:\:\:\:\: (x_α)_{α<τ}\mapsto (x_{φ(α)})_{α<τ}}$:
$\bullet$ is a $(ψ,λ)-$derivation if and only if there exists $\mathsf{r}\in{\mathbb C}^τ$ with $ψ={\mathsf r}σ_φ\restriction_{\ell^p(τ)}$ and $λ=((1)_{α<τ}-{\mathsf r})σ_φ\restriction_{\ell^p(τ)}$,
$\bullet$ is a $ψ-$derivation if and only if $ψ=\frac12σ_φ\restriction_{\ell^p(τ)}$,
$\bullet$ is not a (Jordan, Jordan triple) derivation,
$\bullet$ is a generalized (Jordan, Jordan triple) derivation if and only if $φ=id_τ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_02996 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generalized shifts through derivations' concept in $\ell^p(τ)$ spaces Arzanesh, Safoura Shirazi, Fatemah Ayatollah Zadeh Hosseini, Arezoo Functional Analysis 47B47 In the following text for $p\in[1,\infty]$, nonzero cardinal number $τ$, self--map $φ:τ\toτ$ if there exists $N\in\mathbb{N}$ such that $φ^{-1}(α)$ has at most $N$ elements for each $α<τ$, and operators $ψ,λ:\ell^pτ)\to\ell^p(τ)$ we prove the generalized shift $\mathop{σ_φ\restriction_{\ell^p(τ)}:\ell^p(τ)\to\ell^p(τ)\:\:\:\:\:\:\:\:\:}\limits_{\:\:\:\:\:\:\:\:\: (x_α)_{α<τ}\mapsto (x_{φ(α)})_{α<τ}}$: $\bullet$ is a $(ψ,λ)-$derivation if and only if there exists $\mathsf{r}\in{\mathbb C}^τ$ with $ψ={\mathsf r}σ_φ\restriction_{\ell^p(τ)}$ and $λ=((1)_{α<τ}-{\mathsf r})σ_φ\restriction_{\ell^p(τ)}$, $\bullet$ is a $ψ-$derivation if and only if $ψ=\frac12σ_φ\restriction_{\ell^p(τ)}$, $\bullet$ is not a (Jordan, Jordan triple) derivation, $\bullet$ is a generalized (Jordan, Jordan triple) derivation if and only if $φ=id_τ$. |
| title | Generalized shifts through derivations' concept in $\ell^p(τ)$ spaces |
| topic | Functional Analysis 47B47 |
| url | https://arxiv.org/abs/2104.02996 |