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Operator radii of commuting products


Authors: K. Okubo and T. Ando
Journal: Proc. Amer. Math. Soc. 56 (1976), 203-210
MSC: Primary 47A20
DOI: https://doi.org/10.1090/S0002-9939-1976-0405132-6
MathSciNet review: 0405132
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Abstract: Operator radii $ {w_\rho }(T)$ for a bounded linear operator $ T$ on a Hilbert space were introduced in connection with unitary $ \rho $-dilations. We shall be concerned with universal estimates for the ratios

$\displaystyle {w_\rho }(ST)/({w_\sigma }(S) \cdot {w_\rho }(T))$

for commuting operators $ S,T$ and $ \sigma ,\rho > 0$.

References [Enhancements On Off] (What's this?)

  • [1] T. Ando and K. Nishio, Convexity properties of operator radii associated with unitary $ \rho $-dilations, Michigan Math. J. 20(1973), 303-307. MR 0333767 (48:12091)
  • [2] C. A. Berger and J. G. Stampfli, Norm relations and skew dilations, Acta Sci. Math. (Szeged) 28(1967), 191-195. MR 37 #4661. MR 0229083 (37:4661)
  • [3] M. J. Crabb, The powers of an operator of numerical radius one, Michigan Math. J. 18(1971), 253-256. MR 44 #7345. MR 0290160 (44:7345)
  • [4] J. A. R. Holbrook, On the power-bounded operators of Sz.-Nagy and Foias., Acta Sci. Math. (Szeged) 29(1968), 299-310. MR 39 #810. MR 0239453 (39:810)
  • [5] -, Inequalities governing the operator radii associated with unitary $ \rho $-dilations, Michigan Math. J. 18(1971), 149-159. MR 43 #6755. MR 0281036 (43:6755)
  • [6] B. Sz.-Nagy, Products of operators of classes $ {\mathcal{C}_\rho }$, Rev. Roumaine Math. Pures Appl. 13(1968), 897-899. MR 39 #812. MR 0239455 (39:812)
  • [7] B. Sz.-Nagy and C. Foias, On certain classes of power-bounded operators in Hilbert space, Acta Sci. Math. (Szeged) 27(1966), 17-25. MR 33 #6413. MR 0198254 (33:6413)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0405132-6
Keywords: Operator radius, numerical radius, contraction, unitary $ \rho $-dilation, class $ {\mathcal{C}_\rho }$, commuting operators, Hilbert space
Article copyright: © Copyright 1976 American Mathematical Society

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