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Math Help - product of positive operators

  1. #1
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    product of positive operators

    Let V be an inner product space with finite dimension. Suppose that T and U are two positive linear operators. I need an example to show that TU is not necessarily a positive operator.
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  2. #2
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    Re: product of positive operators

    How are you defining positive linear operator?
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  3. #3
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    Re: product of positive operators

    A linear operator T on an inner product space with finite dimension is positive if T is Hermitian and for every \alpha \neq 0, (T\alpha|\alpha) >0 (i.e. inner product of \alpha and T\alpha is positive).
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