The Analogue Of The Group Algebra For Topological Semigroups (research Notes In Mathematics)

Cover......Page 1 Title: The analogue of thegroup algebra fortopological semigroups......Page 2 ISBN 0-273-08610-3......Page 3 Preface......Page 4 Contents......Page 7 1. SEMIGROUPS......Page 9 2. TOPOLOGICAL SEMIGROUPS......Page 10 3. THE ALGEBRA OF BOUNDED RADON MEASURES M(S)......Page 11 4. SOME CONTINUITY PROPERTIES OF RADON MEASURES......Page 17 1. ABSOLUTELY CONTINUOUS MEASURES......Page 19 2. WEAK AND NORM CONTINUOUS TRANSLATIONS OF MEASURES......Page 28 3. EQUI-REGULAR MEASURES......Page 34 4. QUASI-INVARIANT MEASURES......Page 43 5. MULTIPLICATIVE LINEAR FUNCTIONALS AND SEMI CHARACTERS......Page 46 6. NOTES ON REFERENCES......Page 51 1. INTRODUCTION......Page 53 2. THE STRUCTURE OF STIPS......Page 54 3. THE ROLE OF IDEMPOTENTS IN A STIP......Page 59 4. ACTIONS ON NORMED LINEAR SPACES......Page 65 1. UNIFORMLY CONTINUOUS FUNCTIONS......Page 71 2. INVARIANT MEANS......Page 79 3. THE SIZE OF THE DIFFERENCE WUC(S)\WAP(S)......Page 91 4. THE STONE-~ECH COMPACTIFICATION OF A SEMIGROUP......Page 101 5. REGULARITY OF MULTIPLICATION IN SEMIGROUP ALGEBRAS......Page 109 1. CONTINUITY OF MEASURES UNDER TRANSLATION ON A STIP......Page 119 2. MEASURES WITH SEPARABLE ORBITS......Page 123 3. MEASURES VANISHING ON EMACIATED SETS......Page 128 4. LOCALLY QUASI-INVARIANT MEASURES......Page 135 5. CONTINUITY OVER DIRECT TRANSLATES OF COMPACT SETS......Page 137 6. SOME FURTHER NOTES......Page 139 1. REGULARITY·OF MULTIPLICATION IN WEIGHTED SEMIGROUP ALGEBRAS......Page 140 2. EXISTENCE OF APPROXIMATE IDENTITIES......Page 147 3. A FACTORIZABLE BANACH ALGEBRA WITHOUT AN APPROXIMATE IDENTITY......Page 151 4. AMENABILITY OF THE ALGEBRA L^1(S)......Page 152 1. PREREQUISITES......Page 160 2. SEMICHARACTERS......Page 164 3. THE NON-ARCHIMEDEAN MEASURE ALGEBRA M(S)......Page 169 4. THE NON-ARCHIMEDEAN SEMIGROUP ALGEBRA M (S)......Page 173 5. NOTES......Page 180 2. A C-ENERALIZED STONE-WEIERSTRASS THEOREM......Page 182 3. A GENERALIZATION OF THE RIESZ-REPRESENTATION THEOREM......Page 184 2. WEAKLY COMPACT SUBSETS OF M(X)......Page 186 3. WEAKLY COMPACT SUBSETS OF C(X)......Page 187 Bibliography......Page 190 Index of symbols......Page 199