Hilbert Spaces

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


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.


Hilbert Space Bounded Linear Operator Normed Linear Space Continuous Linear Operator Complex Hilbert Space 
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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

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

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