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This paper provides a method to study the non-negativity of certain linearoperators, from other operators with similar spectral properties. If these newoperators are formally self-adjoint and non-negative, we can study the complexpowers using an appropriate locally convex space. In this case, the initialoperator also will be non-negative and we will be able to study their powers.In particular, we have applied this method to Bessel-type operators.

Distributional fractional powers of similar operators. Applications to the Bessel operators