03235nam a22002297a 4500 56322 56322 20200124122603.0 200124b ||||| |||| 00| 0 eng d 3540901361 Donated by Mathematics Department 515.7 HOL Richard B Holmes Geometric Functional Analysis and its Applications /Richard B Holmes New York, NY : Springer New York , 1975. Various Pages ;24 cm. 00 I Convexity in Linear Spaces -- ʹ 1. Linear Spaces -- ʹ 2. Convex Sets -- ʹ 3. Convex Functions -- ʹ 4. Basic Separation Theorems -- ʹ 5. Cones and Orderings -- ʹ 6. Alternate Formulations of the Separation Principle -- ʹ 7. Some Applications -- ʹ 8. Extremal Sets -- Exercises -- II Convexity in Linear Topological Spaces -- ʹ 9. Linear Topological Spaces -- ʹ10. Locally Convex Spaces -- ʹ11. Convexity and Topology -- ʹ12. Weak Topologies -- ʹ13. Extreme Points -- ʹ14. Convex Functions and Optimization -- ʹ15. Some More Applications -- Exercises -- III Principles of Banach Spaces -- ʹ16. Completion, Congruence, and Reflexivity -- ʹ17. The Category Theorems -- ʹ18. The Smulian Theorems -- ʹ19. The Theorem of James -- ʹ20. Support Points and Smooth Points -- ʹ21. Some Further Applications -- Exercises -- IV Conjugate Spaces and Universal Spaces -- ʹ22. The Conjugate of C(?,?) -- ʹ23. Properties and Characterizations of Conjugate Spaces -- ʹ24. Isomorphism of Certain Conjugate Spaces -- ʹ25. Universal Spaces - This book has evolved from my experience over the past decade in teaching and doing research in functional analysis and certain of its appli cations. These applications are to optimization theory in general and to best approximation theory in particular. The geometric nature of the subjects has greatly influenced the approach to functional analysis presented herein, especially its basis on the unifying concept of convexity. Most of the major theorems either concern or depend on properties of convex sets; the others generally pertain to conjugate spaces or compactness properties, both of which topics are important for the proper setting and resolution of optimization problems. In consequence, and in contrast to most other treatments of functional analysis, there is no discussion of spectral theory, and only the most basic and general properties of linear operators are established. Some of the theoretical highlights of the book are the Banach space theorems associated with the names of Dixmier, Krein, James, Smulian, Bishop-Phelps, Brondsted-Rockafellar, and Bessaga-Pelczynski. Prior to these (and others) we establish to two most important principles of geometric functional analysis: the extended Krein-Milman theorem and the Hahn Banach principle, the latter appearing in ten different but equivalent formula tions (some of which are optimality criteria for convex programs). In addition, a good deal of attention is paid to properties and characterizations of conjugate spaces, especially reflexive spaces. Mathematics ;Functional analysis Richard B Holmes MDL 0 0 ddc 0 0 MDL MDL 2020-01-24 Donated by Mathematics Department 0.00 0 515.7 HOL M176 2020-01-24 00:00:00 2020-01-24 MDL