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The Spectral Theorem, Stable Subspaces and v. Neumann Algebras

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Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL,volume 198)

Abstract

The general remarks given in the beginning of the last chapter apply equally well at present. The main object is to prove the spectral theorem for self adjoint continuous operators in Hilbert space and introduce the reader to the elements of the theory of v. Neumann algebras. The contents of Sections 1 and 2 are needed only for the proof of the spectral theorem, which is given in Section 3. Almost all the material presented in Sections 4, 5 and 6 will be used later. Most of it can be read without being familiar with the contents of Chapter I. Similarly an understanding of the statement of the spectral theorem requires no background in Banach algebra theory but the proof relies heavily on the fundamental results discussed in Chapter I.

Keywords

  • Hilbert Space
  • Vector Lattice
  • Banach Lattice
  • Topological Vector Space
  • Adjoint Operator

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.

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© 1973 Springer-Verlag Berlin Heidelberg

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Gaal, S.A. (1973). The Spectral Theorem, Stable Subspaces and v. Neumann Algebras. In: Linear Analysis and Representation Theory. Die Grundlehren der mathematischen Wissenschaften, vol 198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80741-1_3

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  • DOI: https://doi.org/10.1007/978-3-642-80741-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-80743-5

  • Online ISBN: 978-3-642-80741-1

  • eBook Packages: Springer Book Archive