Abstract
This chapter is devoted to several results the proofs of which are based on a theorem known as the Hahn-Banach theorem (due to H. Hahn, 1927, and S. Banach, 1929). Most of these results, as well as the Hahn-Banach theorem itself, are extension theorems dealing with extension of a (linear) operator from a linear subspace to the entire space, thereby preserving certain properties of the operator (such as, for example, positivity or norm boundedness). To prove the Hahn-Banach theorem it is necessary to accept a certain axiom about partially ordered sets, called Zorn’s lemma. We formulate the axiom. The definition of a chain and of a maximal element in a partially ordered set are given in section 1.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Zaanen, A.C. (1997). Results with the Hahn-Banach Theorem. In: Introduction to Operator Theory in Riesz Spaces. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60637-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-60637-3_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64487-0
Online ISBN: 978-3-642-60637-3
eBook Packages: Springer Book Archive