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Unitarily Invariant Operator Norms

Published online by Cambridge University Press:  20 November 2018

C.-K. Fong  and
J. A. R. Holbrook
C.-K. Fong
Affiliation:
University of Toronto, Toronto, Ontario
J. A. R. Holbrook
Affiliation:
University of Guelph, Guelph, Ontario
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1.1. Over the past 15 years there has grown up quite an extensive theory of operator norms related to the numerical radius

1

of a Hilbert space operator T. Among the many interesting developments, we may mention:

(a) C. Berger's proof of the “power inequality”

2

(b) R. Bouldin's result that

3

for any isometry V commuting with T;

(c) the unification by B. Sz.-Nagy and C. Foias, in their theory of ρ-dilations, of the Berger dilation for T with w(T) ≤ 1 and the earlier theory of strong unitary dilations (Nagy-dilations) for norm contractions;

(d) the result by T. Ando and K. Nishio that the operator radii wρ(T) corresponding to the ρ-dilations of (c) are log-convex functions of ρ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 35 , Issue 2 , 01 April 1983 , pp. 274 - 299
Copyright
Copyright © Canadian Mathematical Society 1983

References

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