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On the Maximum Principle of Ky Fan

Published online by Cambridge University Press:  20 November 2018

M. Marcus  and
B. N. Moyls
M. Marcus
Affiliation:
University of British Columbia
B. N. Moyls
Affiliation:
University of British Columbia
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In 1951 Fan (1) proved the following interesting extreme value result: Let A1, … , Am be completely continuous operators on a Hilbert space . For be the characteristic roots of Aσ* Aσ. Then, for any positive integer k,

(1),

(2),

where both maxima are taken over all unitary operators U1, … , Um and all sets of k orthonormal (o.n.) vectors.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 313 - 320
Copyright
Copyright © Canadian Mathematical Society 1957

References

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