matmessМатематические заметки СВФУMathematical notes of NEFU2411-93262587-876XСеверо-Восточный федеральный университет имени М.К. Аммосова10.25587/2411-9326-2024-1-70-80matmess-115Research ArticleМАТЕМАТИКАStructured pseudospectrum and structured essential pseudospectrum of closed linear operator pencils on ultrametric Banach spacesStructured pseudospectrum and structured essential pseudospectrum of closed linear operator pencils on ultrametric Banach spacesEttaybJ.EttaybJ.2024300320243117080Copyright © Ettayb J., 20242024Ettayb J.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://matmess.elpub.ru/jour/article/view/115

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We introduce and study the structured pseudospectrum and the essential pseudospectrum of closed linear operator pencils on ultrametric Banach spaces. We establish a characterization of the structured pseudospectrum of closed linear operator pencils and relationship between the structured pseudospectrum and the structured pseudospectrum of closed linear operator pencils on ultrametric Banach spaces. Many characterizations of structured essential pseudospectra of operators, such as the structured essential pseudospectrum of closed linear operator pencils, is invariant under per- turbation of completely continuous linear operators on ultrametric Banach spaces over Qp. Finally, we give some illustrative examples.

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