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A note on normal operators

Published online by Cambridge University Press:  24 October 2008

S. J. Bernau  and
F. Smithies
S. J. Bernau
Affiliation:
Churchill College, Cambridge and St John's College, Cambridge
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Extract

We recall that a bounded linear operator T in a Hilbert space or finite-dimensional unitary space is said to be normal if T commutes with its adjoint operator T*, i.e. TT* = T*T. Most of the proofs given in the literature for the spectral theorem for normal operators, even in the finite-dimensional case, appeal to the corresponding results for Hermitian or unitary operators.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 4 , October 1963 , pp. 727 - 729
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Halmos, P. R.Introduction to Hilbert space and the theory of spectral multiplicity (Chelsea; New York, 1951).Google Scholar
(2)Taylor, A. E.Introduction to functional analysis (Wiley; New York and London, 1958).Google Scholar