NUMERICAL RANGE AND POSITIVE BLOCK MATRICES
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We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range $W(X)$ of the off-diagonal block $X$ , especially the distance $d$ from $0$ to $W(X)$ . A special consequence is an estimate, $$\begin{eqnarray}\text{diam}\,W\left(\left[\begin{array}{@{}cc@{}}A & X\\ X^{\ast } & B\end{array}\right]\right)-\text{diam}\,W\biggl(\frac{A+B}{2}\biggr)\geq 2d,\end{eqnarray}$$ between the diameters of the numerical ranges for the full matrix and its partial trace.
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1971 ◽
Vol 12
(2)
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pp. 110-117
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1985 ◽
Vol 97
(2)
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pp. 321-324
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1979 ◽
Vol 85
(2)
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pp. 325-333
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1986 ◽
Vol 28
(1)
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pp. 37-45
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1978 ◽
Vol 30
(02)
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pp. 419-430
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1974 ◽
Vol 17
(2)
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pp. 295-296
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