Geodesic
Unitarily Invariant Operator Norms
Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 274-299

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Fong, C.-K.; Holbrook, J. A. R. Unitarily Invariant Operator Norms. Canadian journal of mathematics, Tome 35 (1983) no. 2, pp. 274-299. doi: 10.4153/CJM-1983-015-3
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[1] 1. Ando, T., Structure of operators with numerical radius one, Acta Sci. Math. 34 (1973), 11–15. Google Scholar

[2] 2. Ando, T., Topics in dilation theory, Sapporo (1973). Google Scholar

[3] 3. Ando, T. and Nishio, K., Convexity properties of operator radii associated with unitaryp-dilations, Michigan Math. J. 20 (1973), 303–307. Google Scholar

[4] 4. Ando, T. and Okubo, K., Operator radii of commuting products, Proc. Amer. Math. Soc. 56 (1976), 203–210. Google Scholar

[5] 5. Berger, C. A., A strange dilation theorem, Notices Amer. Math. Soc. 12 (1965), 590. Google Scholar

[6] 6. Berger, C. A. and Stampfli, J. G., Norm relations and skew dilations, Acta Sci. Math. 28 (1967), 191–195. Google Scholar

[7] 7. Berger, C. A. and Stampfli, J. G., Mapping theorems for the numerical range, Amer. J. Math. 89 (1967), 1047–1055. Google Scholar

[8] 8. Bonsall, F. F. and Duncan, J., Numerical ranges of operators on normed spaces and of elements of normed algebras (Cambridge U. P., 1971). Google Scholar

[9] 9. Bonsall, F. F. and Duncan, J., Numerical ranges II (Cambridge U. P., 1973). Google Scholar

[10] 10. Bouldin, R., The numerical range of a product II, J. Math. Anal. Appl. 33 (1971), 212–219. Google Scholar

[11] 11. Holbrook, J. A. R., Multiplicative properties of the numerical radius in operator theory, J. reine angew. Math. 237 (1969), 166–174. Google Scholar

[12] 12. Holbrook, J. A. R., On the power-bounded operators of Sz.-Nagy and Foias, Acta Sci. Math. 29 (1968), 299–310. Google Scholar

[13] 13. Katznelson, Y., An introduction to harmonic analysis (Wiley, 1968). Google Scholar

[14] 14. Palmer, T. W., Characterizations of C*-algebras II, Trans. Amer. Math. Soc. 148 (1970), 577–588. Google Scholar

[15] 15. Pearcy, C., An elementary proof of the power inequality for the numerical radius, Michigan Math. J. 13 (1966), 289–291. Google Scholar

[16] 16. Schatten, R., Norm ideals of completely continuous operators (Springer, 1960). Google Scholar

[17] 17. Sz.-Nagy, B. and Foias, C., Harmonic analysis of operators on Hilbert space (North-Holland, 1970). Google Scholar

[18] 18. Williams, J. P., Schwarz norms for operators, Pacific J. Math. 24 (1968), 181–188. Google Scholar

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