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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Operator radii of commuting products

Authors: K. Okubo and T. Ando
Journal: Proc. Amer. Math. Soc. 56 (1976), 203-210
MSC: Primary 47A20
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 \[ {w_\rho }(ST)/({w_\sigma }(S) \cdot {w_\rho }(T))\] for commuting operators $S,T$ and $\sigma ,\rho > 0$.

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Keywords: Operator radius, numerical radius, contraction, unitary <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img5.gif" ALT="$\rho$">-dilation, class <!– MATH ${\mathcal {C}_\rho }$ –> <IMG WIDTH="26" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${\mathcal {C}_\rho }$">, commuting operators, Hilbert space
Article copyright: © Copyright 1976 American Mathematical Society