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Unitary Equivalence in Pairwise Spectral Analysis

Published online by Cambridge University Press:  22 January 2016

Edward W. Barankin*
Affiliation:
University of California, Berkeley
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It is a privilege to share in the honoring of Professor Katuzi Ono on this occasion, It would be enough to be simply putting in evidence my high regard for a good and dear friend. But there is so very much more than that here. It is an opportunity for me to declare my esteem for the kind of mathematician who looks at his field from the outside as well as the inside; who sees the richness of all experience and seeks its instruction to know better and better the meaning of mathematics ; who by the example of his own life urges young, coming scientists to the more productive path of an uncompartmentalized personality. Katuzi Ono is all of these.

In the pairwise spectral analysis of two projections F and G (see [1, §4] of the References) there are determined two resolutions of the identity, EF-and EG, which are spectral measures on the Borel interval [0, 1], and which are, in fact, the spectral measures of the Hermitian operators SF and SG of (1. 6) below.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[1] Barankin, Edward W., “Toward the mathematics of a general theory of behavior, I: the lattice Annals of the Institute of Statistical Mathematics, Tokyo, Vol. 21, No. 3, 1969, pp. 421456.CrossRefGoogle Scholar
[2] Strasen, Stephen M., Flanking in the Wide Sense, doctoral dissertation, University of California, Berkeley, November, 1968.Google Scholar