Open AccessPseudospectra in a non-Archimedean Banach space and essential pseudospectra in Eω
Author(s) -
Aymen Ammar,
Ameni Bouchekoua,
Aref Jeribi
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1912961a
Subject(s) - mathematics , hilbert space , banach space , linear operators , pure mathematics , linear map , operator (biology) , space (punctuation) , mathematical analysis , computer science , operating system , biochemistry , chemistry , repressor , transcription factor , bounded function , gene
In this work, we introduce and study the pseudospectra and the essential pseudospectra of linear operators in a non-Archimedean Banach space and in the non-Archimedean Hilbert space E?, respectively. In particular, we characterize these pseudospectra. Furthermore, inspired by T. Diagana and F. Ramaroson [12], we establish a relationship between the essential pseudospectrum of a closed linear operator and the essential pseudospectrum of this closed linear operator perturbed by completely continuous operator in the non-Archimedean Hilbert space E?.