P-adic functional analysis

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Front PREFACE CONTENTS CONTRIBUTORS 1. ON BISEPARATING ISOMORPHISMS BETWEEN REAL COMPACT SPACES 1. INTRODUCTION 2. BISEPARATING ISOMORPHISMS 3. AUTOMATIC CONTINUITY REFERENCES 2. EXTENDING ISOMETRIES BETWEEN NONARCHIMEDEAN SPACES, WITHOUT THE AXIOM OF CHOICE REFERENCES 3. NON-ARCHIMEDEAN BANACH SPACES OVER TRIVIALLY VALUED FIELDS 0. NOTATIONS AND PRELIMINARIES 1. GENERALITIES 2. ORTHOGONALITY IN (E, II · II) 3. t-ORTHOGONALITY IN (E, II · II) 4. LINEAR MAPS AND EXTENSION THEOREMS 5. THE NORM OF A LINEAR MAP REFERENCES 4. TWO NEW OPERATOR IDEALS IN NON-ARCHIMEDEAN BANACH SPACES 1. INTRODUCTION 2. PRELIMINARIES 3. GENERAL FACTS ABOUT OPERATOR IDEALS 4. LIMITED OPERATORS 5. PELCZVNSKI OPERATORS AND VLADIMIRSKil OPERATORS REFERENCES 5. ULTRAMETRIC ALMOST PERIODIC LINEAR REPRESENTATIONS 1. ALMOST PERIODIC FUNCTIONS 2. BANACH COMODULES OVER AP(G, K) 3. INTEGRALS FOR THE HOPF ALGEBRA AP(G, K) REFERENCES 6. NON-ARCHIMEDEAN THEORY OF PROBABILITY 1. INTRODUCTION 2. GENERAL PRINCIPLE OF THE STATISTICAL STABILIZATION 3. CALCULUS OF PROBABILITIES 4. p-ADIC STATISTICAL SIMULATION 5. WHAT CAN WE DO WITH P-ADIC PROBABILITIES? 6. THE FIRST STEP TO THE p-ADIC THEORY OF INFORMATION 7. ACKNOWLEDGE REFERENCES 7. SEPARATING MAPS ON RINGS OF CONTINUOUS FUNCTIONS 0. NOTATION 1. STONE-BANACH MAPS 2. EVALUATION MAPS 3. THE SUPPORT FUNCTION 4. CONTINUITY OF WEAKLY SEPARATING MAPS 5. THE SET Sc OF CONTINUITY POINTS 6. AUTOMATIC CONTINUITY RESULTS REFERENCES 8. A PROPERTY OF THE STRICT TOPOLOGY ON Cb(X) 1. INTRODUCTION 2. THE THEOREM REFERENCES 9. NON-ARCHIMEDEAN ANALYSIS WHEN THE VALUE GROUP HAS A NON-ARCHIMEDEAN ORDER 0. INTRODUCTION 1. NORMED SPACES. 2. THE NORM INDUCED BY A HERMITIAN FORM. 0RTHOMODULAR SPACES. 3. THE PRINCIPLE OF UNIFORM BOUNDEDNESS. (BANACH-STEINHAUS). 4. REFLEXIVITY AND THE HAHN-BANACH EXTENSION PROPERTY IN GROSS-KELLER-KUNZI SPACES. REFERENCES 10. MODULES OF COUNTABLE TYPE 1. INTRODUCTION 2. BK-MODULES 3. NORMED BK-MODULES 4. GENERATORS 5. THE PROOF OF THE STATEMENT 6. THE LOCALLY CONVEX CASE REFERENCES 11. TENSOR PRODUCT AND p-ADIC VECTOR VALUED CONTINUOUS FUNCTIONS 1. PRELIMINARIES 2. TENSOR PRODUCT AND SPACES OF CONTINUOUS FUNCTIONS 3. TENSOR PRODUCT, REFLEXIVITY AND SPHERICAL COMPLETENESS. REFERENCES 12. SIMULTANEOUS APPROXIMATION AND INTERPOLATION IN p-ADIC ANALYSIS REFERENCES 13. THE EQUALIZATION OF p-ADIC BANACH SPACES AND COMPACTOIDS Part One 1. BANACH SPACES VERSUS COMPACTOIDS, AN ANTI-EQUIVALENCE 2. TERMINOLOGY 3. THE WEAK STAR UNIT BALL OF E' 4. THE ANTI-EQUIVALENCE Part Two 5. BANACH SPACES VERSUS COMPACTOIDS APPLICATIONS 6. DECOMPOSITIONS IN BK AND CK 7. STABILITY OF COMPACTOIDS UNDER INJECTIONS 8. STABILITY OF COMPACTOIDS UNDER (ALMOST) SURJECTIONS 9. ALMOST OPENNESS OF ALMOST SURJECTIONS BETWEEN COMPACTOIDS 10. WHICH SURJECTIONS BETWEEN COMPACTOIDS ARE OPEN? 11. REFLEXIVITY 12. ORTHOGONAL BASES REFERENCES 14. THE P-ADIC MOMENT PROBLEM 1. INTRODUCTION 2. F-SEQUENCES 3. PROOFS OF THEOREMS 1 AND 2 4. EXAMPLES REFERENCES 15. ASYMPTOTICALLY ORTHOGONAL SEQUENCES 1. LARGE SETS AND ASYMPTOTIC ORTHOGONALITY 2. SEMI-FREDHOLM OPERATORS 3. OPERATORS PRESERVING ASYMPTOTIC ORTHOGONALITY 4. PSEUDOREFLEXIVE SPACES 5. WHAT HAPPENS IF IIEII \notsubset cl(IKI) REFERENCES