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(2.1) Moreover, this map preserves positivity when the multiplier is a positive operator.
The resulting integral is a positive operator since each (A_{t}) is positive and each (Phi_{t}) preserves positivity.
Choose a positive operator (Tin L H)).
Let T be a positive operator.
If and is a positive operator on, then (2.12).
It follows that T is also a positive operator.
Finally, we show that (mathcal{T}) is a positive operator.
We present some relationships between the order and ring ideals generated by a positive operator.
It is well known that is a positive operator on with domain.
For a positive operator A in E the following result was established in papers [36, 37].
for each with (c) If and is a positive operator on, then (2.12) .
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