Abstract
In this chapter we shall study both real and complex Banach spaces X such that X* is linearly isometric to an abstract L1 space. We call such spaces L1-predual spaces. There are several classes of classical Banach spaces which have this property (e. g. abstract M spaces and spaces of the type C(T,ℂ). Lindenstrauss was the first one to undertake a systematic study of them (although Grothendieck did study certain types of them, the so called G spaces). In [182] he developed the beginnings of a general structure theory for the real case and has also made many other contributions to the area (see [175], [176], [186], [187], [190], and [193]). Recently interest in the complex case has brought about some significant results (see [289], [291], [292], [293], and [294]). We shall also present some of these, especially in section 23.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1974 Springer-Verlag Berlin · Heidelberg
About this chapter
Cite this chapter
Lacey, H.E. (1974). L1-Predual Spaces. In: The Isometric Theory of Classical Banach Spaces. Die Grundlehren der mathematischen Wissenschaften, vol 208. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-65762-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-65762-7_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-65764-1
Online ISBN: 978-3-642-65762-7
eBook Packages: Springer Book Archive