A Remark on the Respect of Adjoint Operator

At the beginning of this article, the comparison is made between the features of the adjoint operators in Hilbert space and those of the adjoint operators in Banach space. Although some similarities exist in their adjoint, there also exist some differences owing to the different definitions of their respective adjoint operators. Then, the two adjoint operators are linked by means of building conjugate linear isomorphisms. At last, the relationship is set up between a bounded linear operator on a normal space and its second adjoint operator in the light of the canonical imbedding.