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This book focuses on the theory of linear operators on non-Archimedean Banach spaces. The topics treated in this book range from a basic introduction to non-Archimedean valued fields, free non-Archimedean Banach spaces, bounded and unbounded linear operators in the non-Archimedean setting, to the spectral theory for some classes of linear operators. The theory of Fredholm operators is emphasized and used as an important tool in the study of the spectral theory of non-Archimedean operators. Explicit descriptions of the spectra of some operators are worked out. Moreover, detailed background materials on non-Archimedean valued fields and free non-Archimedean Banach spaces are included for completeness and for reference.

The readership of the book is aimed toward graduate and postgraduate students, mathematicians, and non-mathematicians such as physicists and engineers who are interested in non-Archimedean functional analysis. Further, it can be used as an introduction to the study of non-Archimedean operator theory in general and to the study of spectral theory in other special cases.

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Preface.-1. Non-Archimedean Valued Field.-2. Non-Archimedean Banach Spaces.-3. Bounded Linear Operators in Non-Archimedean Banach Spaces.-4. The Vishik Spectral Theorem.-5. Spectral Theory for Perturbations of Bounded Diagonal Linear Operators.-6. Unbounded Linear Operators.-7. Spectral Theory for Perturbations of Unbounded Linear Operators.-References.-Index.

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"This book presents some of the authors´ recent work on continuous linear operators on non-archimedean Banach space as well as their spectral theory. ... The book can be recommended to beginners as an introduction to non-archimendean operator theory." (Bertin Diarra, Mathematical Reviews, January, 2017)
"The book is intended as an introduction to the non-Archimedean operator theory ´for graduate and postgraduate students, mathematicians, and non-mathematicians such as physicists and engineers who are interested in functional analysis in the non-Archimedean context´. Of course, expecting the readership being so wide, the authors make the exposition as elementary as possible." (Anatoly N. Kochubei, zbMATH 1357.47002, 2017)

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