Is it obligatory for someone who has lost a trust (amana) to pay its value to its owner if he does not remember whether he had received it or not?

As long as you are certain that you took possession of the trust, the default is that it remains in your possession unless its retrieval is proven, because certainty is not dispelled by doubt. The depositor is not allowed to demand compensation from you unless the trust was lost as a result of your transgression or negligence in safeguarding it.