Operator radii of commuting products

Okubo, K.; Ando, T.

doi:10.1090/S0002-9939-1976-0405132-6

Operator radii of commuting products
HTML articles powered by AMS MathViewer

by K. Okubo and T. Ando PDF

Proc. Amer. Math. Soc. 56 (1976), 203-210 Request permission

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 \[ {w_\rho }(ST)/({w_\sigma }(S) \cdot {w_\rho }(T))\] for commuting operators $S,T$ and $\sigma ,\rho > 0$.

References

Tsuyoshi Ando and Katsuyoshi Nishio, Convexity properties of operator radii associated with unitary $\rho$-dilations, Michigan Math. J. 20 (1973), 303–307. MR 333767
C. A. Berger and J. G. Stampfli, Norm relations and skew dilations, Acta Sci. Math. (Szeged) 28 (1967), 191–195. MR 229083
Michael J. Crabb, The powers of an operator of numerical radius one, Michigan Math. J. 18 (1971), 253–256. MR 290160
John A. R. Holbrook, On the power-bounded operators of Sz.-Nagy and Foiaş, Acta Sci. Math. (Szeged) 29 (1968), 299–310. MR 239453
John A. R. Holbrook, Inequalities governing the operator radii associated with unitary $\rho$-dilations, Michigan Math. J. 18 (1971), 149–159. MR 281036
Béla Sz.-Nagy, Products of operators of classes $C_{\rho }$, Rev. Roumaine Math. Pures Appl. 13 (1968), 897–899. MR 239455
Béla Sz.-Nagy and Ciprian Foiaş, On certain classes of power-bounded operators in Hilbert space, Acta Sci. Math. (Szeged) 27 (1966), 17–25. MR 198254