"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)

• 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.

"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)

• 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.