The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra
UDC 517.5 We establish the relationship between the S-spectrum of $fg$ and the S-spectrum of $\alpha f+\beta g,$ where $f$ and $g$ are two idempotents on a two-sided quaternionic Banach algebra $\mathcal{A}$ and $\alpha, \beta\in\mathbb{R}.$ We also study the invertibility of linear combinations of...
Збережено в:
| Дата: | 2026 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/8410 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513066521722880 |
|---|---|
| author | Moulaharabbi, Somayya Barraa, Mohamed Moulaharabbi, Somayya Barraa, Mohamed |
| author_facet | Moulaharabbi, Somayya Barraa, Mohamed Moulaharabbi, Somayya Barraa, Mohamed |
| author_sort | Moulaharabbi, Somayya |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:35:54Z |
| description | UDC 517.5
We establish the relationship between the S-spectrum of $fg$ and the S-spectrum of $\alpha f+\beta g,$ where $f$ and $g$ are two idempotents on a two-sided quaternionic Banach algebra $\mathcal{A}$ and $\alpha, \beta\in\mathbb{R}.$ We also study the invertibility of linear combinations of idempotents on $\mathcal{A}.$ To do this, we define the complexification $\mathcal{A}_c$ of $\mathcal{A},$ which is regarded as a real Banach algebra, and establish the relationship between the S-spectrum of $a \in \mathcal{A}$ and the spectrum of $a$ as an element of the complexification $\mathcal{A}_c.$ |
| doi_str_mv | 10.3842/umzh.v77i11.8410 |
| first_indexed | 2026-03-24T03:38:46Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8410 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:46Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-84102026-03-21T13:35:54Z The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra Moulaharabbi, Somayya Barraa, Mohamed Moulaharabbi, Somayya Barraa, Mohamed two-sided quaternionic Banach algebra; Idempotents; S-spectrum UDC 517.5 We establish the relationship between the S-spectrum of $fg$ and the S-spectrum of $\alpha f+\beta g,$ where $f$ and $g$ are two idempotents on a two-sided quaternionic Banach algebra $\mathcal{A}$ and $\alpha, \beta\in\mathbb{R}.$ We also study the invertibility of linear combinations of idempotents on $\mathcal{A}.$ To do this, we define the complexification $\mathcal{A}_c$ of $\mathcal{A},$ which is regarded as a real Banach algebra, and establish the relationship between the S-spectrum of $a \in \mathcal{A}$ and the spectrum of $a$ as an element of the complexification $\mathcal{A}_c.$ УДК 517.5 S-спектр комбінацій ідемпотентів у двобічній кватерніонній банаховій алгебрі Встановлено зв'язок між S-спектром $fg$ і S-спектром $\alpha f+\beta g,$ де $fg$ – два ідемпотенти з двобічної кватерніонної банахової алгебри $\mathcal{A}$ та $\alpha, \beta \in \mathbb{R}.$ Досліджено також можливість обернення лінійних комбінацій ідемпотентів на $\mathcal{A}.$ З цією метою введено комплексифікацію $\mathcal{A}_c$ алгебри $\mathcal{A},$ яку можна розглядати як дійсну банахову алгебру, та встановлено зв'язок між S-спектром $a \in \mathcal{A}$ і спектром $a$ як елемент комплексифікації $\mathcal{A}_c.$ Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8410 10.3842/umzh.v77i11.8410 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 11 (2025); 699–700 Український математичний журнал; Том 77 № 11 (2025); 699–700 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8410/10604 Copyright (c) 2025 Somayya Moulaharabbi, Mohamed Barraa |
| spellingShingle | Moulaharabbi, Somayya Barraa, Mohamed Moulaharabbi, Somayya Barraa, Mohamed The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra |
| title | The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra |
| title_alt | The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra |
| title_full | The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra |
| title_fullStr | The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra |
| title_full_unstemmed | The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra |
| title_short | The S-spectrum of combinations of idempotents on two-sided quaternionic Banach algebra |
| title_sort | s-spectrum of combinations of idempotents on two-sided quaternionic banach algebra |
| topic_facet | two-sided quaternionic Banach algebra Idempotents S-spectrum |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8410 |
| work_keys_str_mv | AT moulaharabbisomayya thesspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra AT barraamohamed thesspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra AT moulaharabbisomayya thesspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra AT barraamohamed thesspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra AT moulaharabbisomayya sspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra AT barraamohamed sspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra AT moulaharabbisomayya sspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra AT barraamohamed sspectrumofcombinationsofidempotentsontwosidedquaternionicbanachalgebra |