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Spectral Theory For a Class Of Non-Normal Operators

Published online by Cambridge University Press:  20 November 2018

Harry Gonshor
Harry Gonshor*
Affiliation:
Pennsylvania State University
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1. Introduction. As is well known, the spectral theorem plays an important part in mathematics because of its many applications. Unfortunately, the theorem is valid for normal operators only. In view of this, attempts have been made by several mathematicians to obtain a theorem about a more general class of operators, which will reduce to the ordinary spectral theorem if the operator is normal. Brown (1) has developed a unitary equivalence theory for a certain class of operators.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 449 - 461
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Brown, A., On binormal operators, Amer. J. Math., 76 (1954), 414–434.Google Scholar
2. Gonshor, H., Spectral theorem for a class of non-normal operators, Ph.D. thesis, Harvard University, June 1953.Google Scholar
3. Kaplansky, I., The structure of certain operator algebras, Amer. Math. Soc. Trans., 70 (1951), 219–233.Google Scholar
4. Mitchell, B. E., Unitary transformations, Can. J. Math., 6 (1954), 69–72.Google Scholar
5. von Neumann, J., On rings of operators, reduction theory, Ann. Math., 50 (1949), 401–485.Google Scholar
6. von Neumann, J. and Murray, F. J., On rings of operators IV, Ann. Math., 44 (1943), 772–773.Google Scholar