Unitarily Invariant Operator Norms
- 1 April 1983
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 35 (2) , 274-299
- https://doi.org/10.4153/cjm-1983-015-3
Abstract
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.Keywords
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