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Search: MSC category 47A12 ( Numerical range, numerical radius )

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1. CMB Online first

Rhaly, H. C.
Corrigendum to "Generalized Cesàro Matrices"
This note corrects an error in Theorem 1 of "Generalized Cesàro matrices" Canad. Math. Bull. 27 (1984), no. 4, 417-422.

Keywords:Cesaro operator, Hilbert-Schmidt operator, numerical range
Categories:47B99, 47A12, 47B10, 47B38

2. CMB 2000 (vol 43 pp. 193)

Magajna, Bojan
C$^*$-Convexity and the Numerical Range
If $A$ is a prime C$^*$-algebra, $a \in A$ and $\lambda$ is in the numerical range $W(a)$ of $a$, then for each $\varepsilon > 0$ there exists an element $h \in A$ such that $\norm{h} = 1$ and $\norm{h^* (a-\lambda)h} < \varepsilon$. If $\lambda$ is an extreme point of $W(a)$, the same conclusion holds without the assumption that $A$ is prime. Given any element $a$ in a von Neumann algebra (or in a general C$^*$-algebra) $A$, all normal elements in the weak* closure (the norm closure, respectively) of the C$^*$-convex hull of $a$ are characterized.

Categories:47A12, 46L05, 46L10

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