Embeddings and Extensions in Analysis

By L.R. Williams and J.H. Wells

Book Overview

The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or, more generally, P in an L space; the other asks for conditions on a pair of metric spaces which will ensure that every contraction or every Lipschitz-Holder map from a subset of X into Y is extendable to a map of the same type from X into Y. The initial work on isometric embedding was begun by K. Menger 1928] with his metric investigations of Euclidean geometries and continued, in its analytical formulation, by I. J. Schoenberg 1935] in a series of papers of classical elegance. The problem of extending Lipschitz-Holder and contraction maps was first treated by E. J. McShane and M. D. Kirszbraun 1934]. Following a period of relative inactivity, attention was again drawn to these two problems by G. Minty's work on non-linear monotone operators in Hilbert space 1962]; by S. Schonbeck's fundamental work in characterizing those pairs (X, Y) of Banach spaces for which extension of contractions is always possible 1966]; and by the generalization of many of Schoenberg's embedding theorems to the P setting of L spaces by Bretagnolle, Dachuna Castelle and Krivine 1966].

• Format: Paperback
• Language: English
• ISBN: 3642660398
• ISBN13: 9783642660399
• Release Date: November 2011
• Publisher: Springer
• Length: 110 Pages
• Weight: 0.46 lbs.
• Dimensions: 0.3" x 6.7" x 9.6"