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
|