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 | References | Similar Articles | Additional Information

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 $\sigma ,\rho > 0$.

- Tsuyoshi Ando and Katsuyoshi Nishio,
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Additional Information

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