Abstract
Some norm inequalities are presented for non- selfadjoint differential operators. First, the resolvent of the introduced non-selfadjoint differential operator using m-sectorial operators in the Hilbert space $$H=L_{2}(\Omega )$$ is established. As application of this new result, the resolvent of the considered operator in the Hilbert space $$H^{\ell }=L_{2}(\Omega )^{\ell }$$ is obtained utilizing some analytic techniques and diagonalizable way.
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