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On the Unitary Equivalence of Certain Classes of Non-Normal Operators. I

Published online by Cambridge University Press:  20 November 2018

P. K. Tam
P. K. Tam*
Affiliation:
New Asia College, Kowloon, Hong Kong
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The following (so-called unitary equivalence) problem is of paramount importance in the theory of operators: given two (bounded linear) operators A1, A2 on a (complex) Hilbert space , determine whether or not they are unitarily equivalent, i.e., whether or not there is a unitary operator U on such that U*A1U = A2. For normal operators this question is completely answered by the classical multiplicity theory [7; 11]. Many authors, in particular, Brown [3], Pearcy [9], Deckard [5], Radjavi [10], and Arveson [1; 2], considered the problem for non-normal operators and have obtained various significant results. However, most of their results (cf. [13]) deal only with operators which are of type I in the following sense [12]: an operator, A, is of type I (respectively, II1, II∞, III) if the von Neumann algebra generated by A is of type I (respectively, II1, II∞, III).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 5 , October 1971 , pp. 849 - 856
Copyright
Copyright © Canadian Mathematical Society 1971

Footnotes

The results of this paper constitute part of the author's doctoral dissertation, written at the University of British Columbia under the supervision of Dr. Donald J. Bures.

References

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