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The closed graph theorem

In: Convergence Structures and Applications to Functional Analysis

Author

Listed:
  • R. Beattie

    (Mount Allison University, Department of Mathematics and Computer Science)

  • H.-P. Butzmann

    (Universität Mannheim, Fakultät für Mathematik und Informatik)

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.

Suggested Citation

  • R. Beattie & H.-P. Butzmann, 2002. "The closed graph theorem," Springer Books, in: Convergence Structures and Applications to Functional Analysis, chapter 0, pages 183-193, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-9942-9_6
    DOI: 10.1007/978-94-015-9942-9_6
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