mathematicsВестник российских университетов. МатематикаRussian Universities Reports. Mathematics2686-96672782-3342Тамбовский государственный университет имени Г.Р. Державина10.20310/2686-9667-2024-29-148-494-516mathematics-128Research ArticleСТАТЬИARTICLESО λ-коммутировании, левом (правом) псевдоспектре и левом (правом) условном псевдоспектре линейных непрерывных операторов на ультраметрических банаховых пространствахOn λ-commuting and left (right) pseudospectrum and left (right) condition pseudospectrum of continuous linear operators on ultrametric Banach spacesЭттайбДжавадEttaybJawadjawad.ettayb@gmail.comРегиональная академия образования и обучения Касабланка Сеттат, Университетская средняя школа Хаммана Аль–ФатавакиРоссияRegional Academy of Education and Training Casablanca Settat, Hamman Al–Fatawaki collegiate High SchoolRussian Federation20242512202429148494516Copyright © Эттайб Д., 20242024Эттайб Д.Ettayb J.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mathematics.elpub.ru/jour/article/view/128

В работе мы демонстрируем некоторые спектральные свойства -коммутирования линейных непрерывных операторов в ультраметрических банаховых пространствах, а также изучаем операторные уравнения и Мы рассматриваем некоторые свойства этих операторных уравнений; приводим иллюстративные примеры. С другой стороны, мы вводим и изучаем левый (правый) псевдоспектр и левый (правый) условный псевдоспектр линейных непрерывных операторов в ультраметрических банаховых пространствах. Мы доказываем, что левые псевдоспектры, связанные с различными являются вложенными множествами, а пересечение всех левых псевдоспектров является левым спектром. Мы выявляем связь между левым (правым) псевдоспектром и левым (правым) условным псевдоспектром. Более того, доказываем еще ряд результатов, касающихся левого (правого) псевдоспектра и левого (правого) условного псевдоспектра линейных непрерывных операторов в ультраметрических банаховых пространствах.

In this paper, we demonstrate some spectral properties of the -commuting of continuous linear operators on ultrametric Banach spaces and we introduce and study the operator equations and We give some properties of these operator equations. Some illustrative examples are provided. On the other hand, we introduce and study the left (right) pseudospectrum and the left (right) condition pseudospectrum of continuous linear operators on ultrametric Banach spaces. We prove that the left pseudospectra associated with various are nested sets and the intersection of all the left pseudospectra is the left spectrum. We give a relationship between the left (right) pseudospectrum and the left (right) condition pseudospectrum. Moreover, many results are proved concerning the left (right) pseudospectrum and the left (right) condition pseudospectrum of continuous linear operators on ultrametric Banach spaces.

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The authors declare that there are no conflicts of interest present.