Counter Examples

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• A non-stable semigroup for which the Lyapunov equation has a bounded invertible, positive solution. Added 23-11-2011.
• The product of a densely defined, invertible operator with a bounded operator need not to be densely defined. Added 24-11-2011.
• The sum of a contraction and a bounded contraction need not to be a contraction. Added 24-3-2009.
• In this example we construct a bounded operator T for which T+B is never invertible for B's having norms suffiently small. Added 24-3-2009.

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