M-Structure and the Banach-Stone Theorem
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736 Ehrhard Behrends
M-Structure and the Banach-Stone Theorem
Springer-Verlag Berlin Heidelberg New York 1979
Author Ehrhard Behrends I. Mathematisches Institut der Freien Universit~.t H~ittenweg 9 D-1000 []erlin 33
AMS Subject Classifications (1978): 46 []20, 46 [] 25, 46 E15
ISBN 3 - 5 4 0 - 0 9 5 3 3 - 0 Springer-Verlag []erlin Heidelberg NewYork ISBN 0 - 3 8 7 - 0 9 5 3 3 - 0 Springer-Verlag NewYork Heidelberg []erlin Library of Congress Cataloging in PublicationData Behrends, Ehrhard,1946M-structure and the Banach-Stonetheorem. (Lecture notes in mathematics; 736) Bibliography: p. Includes indexes. 1. Banachspaces--M-structure. 2. BanachStone theorem. I. Title. II. Series: Lecture notes in mathematics(Berlin) ; ?36. OA3.L28 no. 736 [OA322.2] 510'.8s [515.73] 79-19677 ISBN 0-387-09533-0 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publishei © by Springer-Verlag Berlin Heidelberg 1979 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
I n t r o d u c t i o n
The
mathematical
the
middle
of
lished;
the
The
is
aim
important tions In
the
present
notes
twofold:
this
hope
theory
to
who
have
cussion The
are
sults
not
is o n l y
Stone
contains
functions
many
tors
the
way
in that
like
this
the to
been
users
pub-
the
some
contents
most applica-
Banach-Stone
do r e s e a r c h
the
since
gap.
to p r e s e n t
theorem.
on
these
understandable
field.
possible
proofs
familiar
are
exception
detailed
with
the
Krein-Smulian of unity),
and
the
dis-
elementar~ re-
Alaoglu-Bourbaki
theorem),
and
of
fundamental
theorem,
v
and
the
Boolean
definitions
measures
a CK-space
subspaces
have
and
theory
Hausdorff
centralizer,
CK-spaces
the
has
on
topology
algebras (the
and
proofs
are
of figures.
M-structure
on a compact operators
in this
(Hahn-Banach
examples,
X behaves
certain
of
going
theorem).
theor 7
space
to b e
account
and
to m a k e
the
partitions
M-structure
speaking,
and
been
to p o t e n t i a l
people
(with
theorem,
by a number
Banach
worked
analysis
illustrated
Roughly
new
has
to f i l l
theory
attempted
assumed
representation
text
available
some
yet
Krein-Milman
attempt
generalizations
examples),
(compactifications,
The
has
of f u n c t i o n a l
theorem,
an
self-contained
of s o m e
reader
are
of attracting author
notes
to
theory
comprehensive
of M-structure
the
The
No
to m a k e
subjects those
of M - s t r u c t u r e
sixties.
results
of
the
study
the
to w h a t
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