# Banach Spaces And Descriptive Set Theory: Selected Topics (lecture Notes In Mathematics)

by Pandelis Dodos /
2010 / English / PDF

3.9 MB Download

This volume deals with problems in the structure theory of
separable infinite-dimensional Banach spaces, with a central focus
on universality problems. This topic goes back to the beginnings of
the field and appears in Banach's classical monograph. The novelty
of the approach lies in the fact that the answers to a number of
basic questions are based on techniques from Descriptive Set
Theory. Although the book is oriented on proofs of several
structural theorems, in the main text readers will also find a
detailed exposition of numerous "intermediate" results which are
interesting in their own right and have proven to be useful in
other areas of Functional Analysis. Moreover, several well-known
results in the geometry of Banach spaces are presented from a
modern perspective.

This volume deals with problems in the structure theory of
separable infinite-dimensional Banach spaces, with a central focus
on universality problems. This topic goes back to the beginnings of
the field and appears in Banach's classical monograph. The novelty
of the approach lies in the fact that the answers to a number of
basic questions are based on techniques from Descriptive Set
Theory. Although the book is oriented on proofs of several
structural theorems, in the main text readers will also find a
detailed exposition of numerous "intermediate" results which are
interesting in their own right and have proven to be useful in
other areas of Functional Analysis. Moreover, several well-known
results in the geometry of Banach spaces are presented from a
modern perspective.