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A weaker condition for normality

Published online by Cambridge University Press:  18 May 2009

Ian Doust
Ian Doust
Affiliation:
School of Mathematics, University of New South Wales, Kensington, NSW 2033, Australia
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One of the most important results of operator theory is the spectral theorem for normal operators. This states that a normal operator (that is, a Hilbert space operator T such that T*T= TT*), can be represented as an integral with respect to a countably additive spectral measure,

Here E is a measure that associates an orthogonal projection with each Borel subset of ℂ. The countable additivity of this measure means that if x Eℋ can be written as a sum of eigenvectors then this sum must converge unconditionally.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 2 , May 1994 , pp. 249 - 253
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

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