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Let $ E$ be a complex Hilbert space, with inner product $ \langle\cdot\;, \;\cdot\rangle$ and the norm $ \|\cdot\|$ and let $ \mathcal{L}(E)$ the algebra of all bounded linear operators from $ E$ to $ E$ . Let $ T\in \mathcal{L}(E)$ . We recall for $ S=(S_1,S_2)\in \mathcal{L}(E)^2$ , the numerical range of $ S$Read more