Riesz Spaces, II

✍ Scribed by A.C. Zaanen

• Publisher: North Holland
• Year: 1983
• Tongue: English
• Leaves: 730
• Edition: 1
• Category: Library

✦ Synopsis

While Volume I (by W.A.J. Luxemburg and A.C. Zaanen, NHML Volume 1, 1971) is devoted to the algebraic aspects of the theory, this volume emphasizes the analytical theory of Riesz spaces and operators between these spaces. Though the numbering of chapters continues on from the first volume, this does not imply that everything covered in Volume I is required for this volume, however the two volumes are to some extent complementary.

✦ Table of Contents

Cover
Title
Preface
Table of contents
CHAPTER 11. PRIME IDEAL EXTENSION
76. Prime ideal separation
77. The hull-kernel topology and the dual hull-kernel topology
78. The unique prime ideal extension property
79. Strongly order dense Riesc subspaces
80. Extension theorems
81. Prime ideal extension and the projection property
82. Normal and extremally disconnected lattices
CHAPTER 12. ORDER BOUNDED OPERATORS
83. Order bounded operators
84. Order continuous operators
85. The order dual of a Riesz space
86. Integrals on ideals of measurable functions
87. Integrals and singular linear functionals
88. The largest ideal on which every order bounded operator is order continuous
89. Annihilate¯ and weak topologies
90. The carrier of an order bounded linear functional
91. Complex Riesz spaces
92. Complex order bounded operators
CHAPTER 13. KERNEL OPERATORS
93. Kernel operators
94. The band of absolute kernel operators
95. The band generated by the kernel operators of finite rank
96. Buhvalov's theorem
97. Adjoint operators
98. Dunford's theorem
99. Generalized Carlemaa operators
CHAPTER 14. NORMED RIESZ SPACES
100. Normed Riesz spaces
101. Banach lattices
102. The Banach dual
CHAPTER 15. ORDER CONTINUOUS NORMS
103. Order continuous norms
104. Heyer-Nieberg's lemma and disjoint sequences
105. Ando's theorem and the order topology
106. Order continuity and the order dual
CHAPTER 16. EMBEDDING IN BIDUALS
107. Riesz seminomas and order density of L in L and of L in L
108. More about Riesz seminorms
109. Embedding of L into the order bidual
110. Perfect Riesz spaces
lit. Perfect Banach lattices
112. Banach function spaces
113. The Fatou property
114. Embedding in the Banach bidual; reflexivity
115. Adjoint operators
116. Disjoint sequences and order continuous norms
117. Copies
CHAPTER 17. ABSTRACT Lp-SPACES
118. Riesz spaces wich p-additive norm
119. Semi-H-spaces
120. Representation by a space of measurable functions
121. Representation by a space of continuous functions
CHAPTER 18. COMPACT OPERATORS
122. Compact sets, precompact sets and almost order bounded sets
123. The band of AM-compact operators
124. Theorems of Dodde-Fremlin and Aliprantis-Burkinshaw
125. Compactness, AM-coopactness and semi-compactness
126. Semi-compact operators and order continuity of the operator norm
127. Semi-compact operators and disjoint sequences
128. Semi-compact operators and order projections
129. Semi-compact operators and indices
CHAPTER 19. ORLICZ SPACES AND IRREDUCIBLE OPERATORS
130. Young's inequality
131. Young classes
132. The associate space of an Orlicz space
133. The Banach dual of an Orlicz space
134. The spectrum of an operator in Banach space
135. The Krein-Rutman theorem and the spectral radius
136. Irreducible operators
137. Spectral properties of compact irreducible operators
138. The peripheral spectrum of irreducible positive operators
CHAPTER 20. 0RTH0M0RPHISMS AND f-ALGEBRAS
139. Elementary properties of orthomorphisms
140. The space 0rth(L)
141. Examples of orthomorphisms
142. Properties of f-algebras
143ú The stabilizer of a Riesz space
144. Orthormorphisms in a normed Riesz space
145. Theorems of Radon-Hikodym type
146. The range of an orthomorphism
BIBLIOGRAPHY
SUBJECT INDEX