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Continuous sums of measures and continuous spectra

Published online by Cambridge University Press:  18 May 2009

S. Sankaran
S. Sankaran
Affiliation:
Queen Elizabeth College, London
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Von Neumann's definition of the continuous sum of Hilbert spaces led Segal [3] to define the continuous sum of measures on a measurable space. In this note we employ Segal's definition to investigate the measure structures associated with a self-adjoint transformation of pure point spectrum and a self-adjoint transformation of pure continuous spectrum. While these transformations, as operators on separable Hilbert spaces, are the antithesis of each other we show that in their measure structure one is a particular case of the other.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 1 , January 1965 , pp. 9 - 14
Copyright
Copyright © Glasgow Mathematical Journal Trust 1965

References

REFERENCES

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