Kubzdela A. Selected topics in non-Archimedean Banach spaces. - Torun: Juliusz Schauder centre for nonlinear studies, Nicolaus Copernicus university, 2018. - 170 p. - (Lecture notes in nonlinear analysis; vol.17). - Bibliogr.:p. 165-168. - Ind.: p.169-170. - ISSN 2082-4335 Шифр: (И/В16-К89) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ......................................................... 5 1 Preliminaries ................................................ 7 1.1 Basics .................................................. 7 1.2 Immediate extensions ................................... 20 1.3 The spaces C0(I) and J∞(I) ............................. 25 2 Orthocomplemented subspaces in non-Archimedean Banach spaces ...................................................... 31 2.1 Characterization of orthocomplemented subspaces ........ 33 Thecaseof C0(I) and J∞(I) .............................. 35 The solution of Problem 2.1.2 .......................... 54 2.2 Hilbertian spaces ...................................... 73 General properties of Hilbertian spaces ................ 74 Hilbertian subspaces of J∞ ............................. 76 An example of Cartesian space which is not Hilbertian .. 86 2.3 FDD in non-Archimedean Banach spaces ................... 98 3 Measures of weak noncompactness ............................ 115 3.1 Quantitative Krein's theorem .......................... 116 3.2 Non-Archimedean quantitative Grothendieck's theorem ... 133 3.3 Non-Archimedean quantitative Gantmacher's theorem ..... 140 3.4 Remarks ............................................... 145 4 Isometrics in finite-dimensional normed spaces ............. 147 4.1 The distance preserving mappings ...................... 147 4.2 Mazur-Ulam theorem in non-Archimedean setting ......... 156 4.3 Surjective isometrics ................................ 158 Bibliography .................................................. 165 Index ......................................................... 170