POSITIVE OPERATORS

By EMILY ANDERSON

CONTENTS CHAPTER 1 THE ORDER STRUCTURE OF POSITIVE OPERATORS §1 1 BASIC PROPERTIES OF POSITIVE OPERATORS §1 2 EXTENSIONS OF POSITIVE OPERATORS §1 3 ORDER PROJECTIONS §1 4 ORDER CONTINUOUS OPERATORS §1 5 POSITIVE LINEAR FUNCTIONALS CHAPTER 2 COMPONENTS, HOMOMORPHISMS, AND ORTHOMORPHISMS §2 1 THE COMPONENTS OF A POSITIVE OPERATOR §2 2 LATTICE HOMOMORPHISMS §2 3 ORTHOMORPHISMS CHAPTER 3 TOPOLOGICAL CONSIDERATIONS §3 1 TOPOLOGICAL VECTOR SPACES §3 2 WEAK TOPOLOGIES ON BANACH SPACES §3 3 LOCALLY CONVEX-SOLID RIESZ SPACES CHAPTER 4 BANACH LATTICES §4 1 BANACH LATTICES WITH ORDER CONTINUOUS NORMS §4 2 WEAK COMPACTNESS IN BANACH LATTICES §4 3 EMBEDDING BANACH SPACES §4 4 BANACH LATTICES OF OPERATORS CHAPTER 5 COMPACTNESS PROPERTIES OF POSITIVE OPERATORS §5 1 COMPACT OPERATORS §5 2 WEAKLY COMPACT OPERATORS §5 3 §5 4 DUNFORD–PETTIS OPERATORS BIBLIOGRAPHY