Geometric Functional Analysis and its Applications (Record no. 56322)

MARC details
000 -LEADER
fixed length control field 03235nam a22002297a 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20200124122603.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 200124b ||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 3540901361
028 ## - DISTRIBUTOR NAME
Distributor Name Donated by Mathematics Department
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 515.7 HOL
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Richard B Holmes
245 ## - TITLE STATEMENT
Title Geometric Functional Analysis and its Applications
Statement of responsibility, etc /Richard B Holmes
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc New York, NY
Name of publisher, distributor, etc : Springer New York
Date of publication, distribution, etc , 1975.
300 ## - PHYSICAL DESCRIPTION
Extent Various Pages
Dimensions ;24 cm.
365 ## - TRADE PRICE
Price amount 00
505 ## - FORMATTED CONTENTS NOTE
Contents note <br/>I Convexity in Linear Spaces --<br/>ʹ 1. Linear Spaces --<br/>ʹ 2. Convex Sets --<br/>ʹ 3. Convex Functions --<br/>ʹ 4. Basic Separation Theorems --<br/>ʹ 5. Cones and Orderings --<br/>ʹ 6. Alternate Formulations of the Separation Principle --<br/>ʹ 7. Some Applications --<br/>ʹ 8. Extremal Sets --<br/>Exercises --<br/>II Convexity in Linear Topological Spaces --<br/>ʹ 9. Linear Topological Spaces --<br/>ʹ10. Locally Convex Spaces --<br/>ʹ11. Convexity and Topology --<br/>ʹ12. Weak Topologies --<br/>ʹ13. Extreme Points --<br/>ʹ14. Convex Functions and Optimization --<br/>ʹ15. Some More Applications --<br/>Exercises --<br/>III Principles of Banach Spaces --<br/>ʹ16. Completion, Congruence, and Reflexivity --<br/>ʹ17. The Category Theorems --<br/>ʹ18. The Smulian Theorems --<br/>ʹ19. The Theorem of James --<br/>ʹ20. Support Points and Smooth Points --<br/>ʹ21. Some Further Applications --<br/>Exercises --<br/>IV Conjugate Spaces and Universal Spaces --<br/>ʹ22. The Conjugate of C(?,?) --<br/>ʹ23. Properties and Characterizations of Conjugate Spaces --<br/>ʹ24. Isomorphism of Certain Conjugate Spaces --<br/>ʹ25. Universal Spaces -
520 ## - SUMMARY, ETC.
Summary, etc <br/>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.
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematics
655 ## - INDEX TERM--GENRE/FORM
Genre/form data or focus term ;Functional analysis
700 ## - ADDED ENTRY--PERSONAL NAME
Personal name Richard B Holmes
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Mathematics Departmental Library
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Home library Current library Date acquired Source of acquisition Cost, normal purchase price Total Checkouts Full call number Barcode Date last seen Price effective from Koha item type
    Dewey Decimal Classification     Mathematics Departmental Library Mathematics Departmental Library 24/01/2020 Donated by Mathematics Department 0.00   515.7 HOL M176 24/01/2020 24/01/2020 Mathematics Departmental Library
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