Bases In Banach Spaces I (die Grundlehren Der Mathematischen Wissenschaften In Einzeldarstellungen Mit Besonderer Berucksichtigung Der Anwendungsgebiete Band 154)
by I. M. Singer /
1970 / English / DjVu
4.7 MB Download
This monograph attempts to present the results known today on bases
in Banach spaces and some unsolved problems concerning them.
Although this important part of the theory of Banach spaces has
been studied for more than forty years by numerous mathematicians,
the existing books on functional analysis (e. g. M. M. Day [43], A.
Wilansky [263], R. E. Edwards [54]) contain only a few results on
bases. A survey of the theory of bases in Banach spaces, up to
1963, has been presented in the expository papers [241], [242] and
[243], which contain no proofs; although in the meantime the theory
has rapidly deve1oped, much of the present monograph is based on
those expository papers. Independently, a useful bibliography of
papers on bases, up to 1963, was compiled by B. L. Sanders [219J.
Due to the vastness of the field, the monograph is divided into two
volumes, ofwhich this is the first (see the tab1e of contents).
Some results and problems re1ated to those treated herein have been
de1iberately planned to be inc1uded in Volume 11, where they will
appear in their natural framework (see [242], [243]).
This monograph attempts to present the results known today on bases
in Banach spaces and some unsolved problems concerning them.
Although this important part of the theory of Banach spaces has
been studied for more than forty years by numerous mathematicians,
the existing books on functional analysis (e. g. M. M. Day [43], A.
Wilansky [263], R. E. Edwards [54]) contain only a few results on
bases. A survey of the theory of bases in Banach spaces, up to
1963, has been presented in the expository papers [241], [242] and
[243], which contain no proofs; although in the meantime the theory
has rapidly deve1oped, much of the present monograph is based on
those expository papers. Independently, a useful bibliography of
papers on bases, up to 1963, was compiled by B. L. Sanders [219J.
Due to the vastness of the field, the monograph is divided into two
volumes, ofwhich this is the first (see the tab1e of contents).
Some results and problems re1ated to those treated herein have been
de1iberately planned to be inc1uded in Volume 11, where they will
appear in their natural framework (see [242], [243]).
