Yıl 2020, Cilt 49 , Sayı 2, Sayfalar 854 - 868 2020-04-02

Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity

Ali Akbar ESTAJİ [1] , Ahmad Mahmoudi DARGHADAM [2]


Let $\mathcal F_{\mathcal{P}}( L)$ be the set of all frame maps from $\mathcal P(\mathbb R)$ to $L$, which is an $f$-ring. In this paper, we introduce the subrings $\mathcal F_{{\mathcal{P}}_{\infty}}( L)$ of all frame maps from $\mathcal P(\mathbb R)$ to $L$ which vanish at infinity and $\mathcal F_{{\mathcal{P}}_{K}}( L)$ of all frame maps from $\mathcal P(\mathbb R)$ to $L$ with compact support. We prove $\mathcal F_{{\mathcal{P}}_{\infty}}( L)$ is a subring of $\mathcal F_{\mathcal{P}}(L)$ that may not be an ideal of $\mathcal F_{\mathcal{P}}(L)$ in general and we obtain necessary and sufficient conditions for $\mathcal F_{{\mathcal{P}}_{\infty}}( L)$ to be an ideal of $\mathcal F_{\mathcal{P}}( L)$. Also, we show that $\mathcal F_{{\mathcal{P}}_{K}}( L)$ is an ideal of $\mathcal F_{\mathcal{P}}( L)$ and it is a regular ring. For $f\in\mathcal F_{\mathcal{P}}( L)$, we obtain a sufficient condition for $f$ to be an element of $F_{{\mathcal{P}}_{\infty}}( L)$ ($\mathcal F_{{\mathcal{P}}_{K}}( L)$). Next, we give necessary and sufficient conditions for a frame to be compact. We introduce $\mathcal F_{\mathcal{P}}$-pseudocompact and next we establish equivalent condition for an $\mathcal F_{\mathcal{P}}$-pseudocompact frame to be a compact frame. Finally, we study when for some frame $L$ with $\mathcal F_{{\mathcal{P}}_{\infty}} (L)\neq(0)$, there is a locally compact frame $M$ such that $\mathcal F_{{\mathcal{P}}_{\infty}}( L)\cong\mathcal F_{{\mathcal{P}}_{\infty}}(M)$ and $\mathcal F_{{\mathcal{P}}_{K}}( L)\cong\mathcal F_{{\mathcal{P}}_{K}}(M)$.
Frame, compact frame, locally compact frame, zero-dimensional frame, vanish at infinity
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Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Orcid: 0000-0002-0376-5477
Yazar: Ali Akbar ESTAJİ
Kurum: Hakim Sabzevari University
Ülke: Iran


Orcid: 0000-0001-9416-6041
Yazar: Ahmad Mahmoudi DARGHADAM
Kurum: Hakim Sabzevari University
Ülke: Iran


Tarihler

Yayımlanma Tarihi : 2 Nisan 2020

Bibtex @araştırma makalesi { hujms624015, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2020}, volume = {49}, pages = {854 - 868}, doi = {10.15672/hujms.624015}, title = {Rings of frame maps from \$\\mathcal\{P\}(\\mathbb\{R\})\$ to frames which vanish at infinity}, key = {cite}, author = {ESTAJİ, Ali Akbar and DARGHADAM, Ahmad Mahmoudi} }
APA ESTAJİ, A , DARGHADAM, A . (2020). Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity. Hacettepe Journal of Mathematics and Statistics , 49 (2) , 854-868 . DOI: 10.15672/hujms.624015
MLA ESTAJİ, A , DARGHADAM, A . "Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 854-868 <https://dergipark.org.tr/tr/pub/hujms/issue/53568/624015>
Chicago ESTAJİ, A , DARGHADAM, A . "Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 854-868
RIS TY - JOUR T1 - Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity AU - Ali Akbar ESTAJİ , Ahmad Mahmoudi DARGHADAM Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.624015 DO - 10.15672/hujms.624015 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 854 EP - 868 VL - 49 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.624015 UR - https://doi.org/10.15672/hujms.624015 Y2 - 2019 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity %A Ali Akbar ESTAJİ , Ahmad Mahmoudi DARGHADAM %T Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 2 %R doi: 10.15672/hujms.624015 %U 10.15672/hujms.624015
ISNAD ESTAJİ, Ali Akbar , DARGHADAM, Ahmad Mahmoudi . "Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity". Hacettepe Journal of Mathematics and Statistics 49 / 2 (Nisan 2020): 854-868 . https://doi.org/10.15672/hujms.624015
AMA ESTAJİ A , DARGHADAM A . Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 854-868.
Vancouver ESTAJİ A , DARGHADAM A . Rings of frame maps from $\mathcal{P}(\mathbb{R})$ to frames which vanish at infinity. Hacettepe Journal of Mathematics and Statistics. 2020; 49(2): 868-854.