Geometric Functional Analysis and its Applications is popular PDF and ePub book, written by R. B. Holmes in 2012-12-12, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Geometric Functional Analysis and its Applications can be Read Online from any device for your convenience.
Geometric Functional Analysis and its Applications Book PDF Summary
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.
Detail Book of Geometric Functional Analysis and its Applications PDF
- Author : R. B. Holmes
- Release : 12 December 2012
- Publisher : Springer
- ISBN : 146849371X
- Genre : Mathematics
- Total Page : 0 pages
- Language : English
- PDF File Size : 10,8 Mb
If you're still pondering over how to secure a PDF or EPUB version of the book Geometric Functional Analysis and its Applications by R. B. Holmes, don't worry! All you have to do is click the 'Get Book' buttons below to kick off your Download or Read Online journey. Just a friendly reminder: we don't upload or host the files ourselves.