Hahn-Banach extension theorems

R. Beattie and H.-P. Butzmann
Additional contact information
R. Beattie: Mount Allison University, Department of Mathematics and Computer Science
H.-P. Butzmann: Universität Mannheim, Fakultät für Mathematik und Informatik

Chapter Chapter 5 in Convergence Structures and Applications to Functional Analysis, 2002, pp 153-181 from Springer

Abstract: Abstract The Hahn-Banach problem for convergence vector spaces has its roots in classical functional analysis. Let E be a strict topological 𝓛F-space, M a vector subspace of E with the property that M ∩E n is closed in each E n - such a subspace is called stepwise closed. Further, let φ bea sequentially continuous linear functional on M. Does there exist a (sequentially) continuous linear extension to E? This is a difficult and much researched problem. Subspaces with the property that all sequentially continuous linear functionals have a continuous linear extension have been called well-located in the literature. In Section 5 we show how such spaces are related to the question of the solution of partial differential equations.

Keywords: Banach Space; Vector Space; Closed Subspace; Topological Vector Space; Extension Property (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9942-9_5

Ordering information: This item can be ordered from
http://www.springer.com/9789401599429

DOI: 10.1007/978-94-015-9942-9_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().