POSITIVE OPERATORS

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viii Contents Chapter 4. Banach Lattices 181 §4.1. Banach Lattices with Order Continuous Norms 181 §4.2. Weak Compactness in Banach Lattices 207 §4.3. Embedding Banach Spaces 221 §4.4. Banach Lattices of Operators 254 Chapter 5. Compactness Properties of Positive Operators 273 §5.1. Compact Operators 273 §5.2. Weakly Compact Operators 290 §5.3. L- and M-weakly Compact Operators 316 §5.4. Dunford–Pettis Operators 340 Bibliography 359 Monographs 369 Index 371
Foreword This monograph is a reprint of our original book Positive Operators published in 1985 as volume # 119 in the Pure and Applied Mathematics series of Academic Press. With the exception of correcting several misprints and a few mathematical errors, this edition of the book is identical to the original one. At the end of the book we have listed a collection of monographs that were published after its 1985 publication that contain material and new developments related to the subject matter of this book. West Lafayette and Indianapolis CHARALAMBOS D. ALIPRANTIS May, 2006 OWEN BURKINSHAW ix
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42 1. The Order Structure of Positi
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Components, Homomorphisms, and Orth
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2.1. The Components of a Positive O
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2.2. Lattice Homomorphisms 93 2.2.
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2.2. Lattice Homomorphisms 95 opera
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2.2. Lattice Homomorphisms 97 Proof
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2.2. Lattice Homomorphisms 99 Theor
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2.2. Lattice Homomorphisms 101 Proo
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2.2. Lattice Homomorphisms 103 comp
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2.2. Lattice Homomorphisms 105 Proo
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2.2. Lattice Homomorphisms 107 comp
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2.2. Lattice Homomorphisms 109 (2)
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2.3. Orthomorphisms 111 (e) Present
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2.3. Orthomorphisms 113 T (y) ∈ B
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2.3. Orthomorphisms 115 Proof. Let
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2.3. Orthomorphisms 117 The disjoin
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2.3. Orthomorphisms 119 defines an
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2.3. Orthomorphisms 121 follows fro
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2.3. Orthomorphisms 123 case we hav
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2.3. Orthomorphisms 125 Proof. We c
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2.3. Orthomorphisms 127 be identifi
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2.3. Orthomorphisms 129 is R X . By
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2.3. Orthomorphisms 131 6. Let (P)
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Chapter 3 Topological Consideration
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3.1. Topological Vector Spaces 135
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3.2. Weak Topologies on Banach Spac
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3.3. Locally Convex-Solid Riesz Spa
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Banach Lattices Chapter 4 It is wel
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4.1. Banach Lattices with Order Con
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4.2. Weak Compactness in Banach Lat
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4.3. Embedding Banach Spaces 221 (a
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4.3. Embedding Banach Spaces 223 th
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4.3. Embedding Banach Spaces 225 (3
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4.3. Embedding Banach Spaces 229 (b
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4.3. Embedding Banach Spaces 231 Th
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4.3. Embedding Banach Spaces 233 It
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4.3. Embedding Banach Spaces 235 (1
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4.3. Embedding Banach Spaces 237 ˙
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4.3. Embedding Banach Spaces 239 C
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4.3. Embedding Banach Spaces 241 Pr
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4.3. Embedding Banach Spaces 243 ho
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4.3. Embedding Banach Spaces 245 In
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4.3. Embedding Banach Spaces 247 Le
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4.3. Embedding Banach Spaces 249 ST
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4.3. Embedding Banach Spaces 251 co
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4.3. Embedding Banach Spaces 253 Th
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4.4. Banach Lattices of Operators 2
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Compactness Properties of Positive
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5.1. Compact Operators 275 An opera
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5.1. Compact Operators 277 Proof. L
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5.1. Compact Operators 279 holds fo
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5.1. Compact Operators 281 simplici
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5.1. Compact Operators 283 To this
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5.1. Compact Operators 285 and S2(
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5.1. Compact Operators 287 “roots
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5.1. Compact Operators 289 10. (Loz
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5.2. Weakly Compact Operators 291 (
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5.2. Weakly Compact Operators 293 d
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5.2. Weakly Compact Operators 295 P
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5.2. Weakly Compact Operators 297 N
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5.2. Weakly Compact Operators 299 T
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5.2. Weakly Compact Operators 301 s
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5.2. Weakly Compact Operators 303 F
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5.2. Weakly Compact Operators 305 a
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5.2. Weakly Compact Operators 309 b
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5.4. Dunford-Pettis Operators 341 T
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5.4. Dunford-Pettis Operators 351 y
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5.4. Dunford-Pettis Operators 357 1
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360 Bibliography 15. C. D. Aliprant
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362 Bibliography 61. P. Enflo, A co
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364 Bibliography 104. M. G. Krein a
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366 Bibliography 144. L. C. Moore,
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368 Bibliography 188. A. I. Veksler
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Index AL-space, 194 AM-space, 193,
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Index 373 supporting, 138 gauge, 13
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Index 375 projection band, 35 proje
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