Advertisement

Hilbert Spaces

  • A. Mukherjea
  • K. Pothoven
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG)

Abstract

In this chapter we will study aspects of the theory of Hilbert spaces. Roughly we may say that a Hilbert space is a Banach space whose norm is defined in a particular manner. We shall give a characterization in terms of the norm of those Banach spaces that are actually Hilbert spaces. This well-known result (Proposition 6.2) is due to Jordan and von Neumann.

Keywords

Hilbert Space Bounded Linear Operator Normed Linear Space Continuous Linear Operator Complex Hilbert Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. von Neumann, Allgemeine Eigenwerttheorie Hermitescher Functionaloperen, Math. Ann. 102 49–131 (1929–1930)Google Scholar
  2. J. von Neumann, Mathematische Begründung der Quantenmechanik, Nachr. Ges. Wiss. Göttingen Math.-Phys. KL, 1–57 (1927).Google Scholar
  3. H. Löwig, Komplexe euklidische Räume von beliebiger endlicher oder unendlicher Dimensionzahl, Acta Sei. Math. Szeged 7, 1–33 (1934).Google Scholar
  4. F. Reilich, Spectraltheorie in nichtseparabeln Räumen, Math. Ann. 110, 342–356 (1935).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • A. Mukherjea
    • 1
  • K. Pothoven
    • 1
  1. 1.University of South FloridaTampaUSA

Personalised recommendations