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On the spectral theorem for normal operators

Published online by Cambridge University Press:  24 October 2008

R. G. Douglas  and
Carl Pearcy
R. G. Douglas
Affiliation:
University of Michigan
Carl Pearcy
Affiliation:
University of Michigan
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Extract

It has been known for some time that one can construct a proof of the spectral theorem for a normal operator on a Hilbert space by applying the Gelfand representation theorem to the Abelian von Neumann algebra generated by the normal operator, and using the fact that the maximal ideal space of an Abelian von Neumann algebra is extremely disconnected. This, in fact, is the spirit of the monograph (8). On the other hand, it is difficult to find in print accounts of the spectral theorem from this viewpoint and, in particular, the treatment in (8) uses a considerable amount of measure theory and does not have the proof of the spectral theorem as its main objective.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 393 - 400
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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