The closed graph theorem

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 6 in Convergence Structures and Applications to Functional Analysis, 2002, pp 183-193 from Springer

Abstract: Abstract Closed graph theorems give sufficient conditions to guarantee that a linear mapping with a closed graph is continuous. Time has established this result as one of the fundamental principles of functional analysis. The first version was due to Banach [Ba32] and took place in the setting of Fréchet spaces. This theorem proved to be so useful that great efforts were made over the next decades to increase its scope: to enlarge the classes of spaces which could act as domain spaces and codomain spaces for a closed graph theorem.

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_6

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

DOI: 10.1007/978-94-015-9942-9_6

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 ().