On generalized adjoint Abelian operators on Banach spaces (Q1084624)

The Riesz representation theorem is proved in a generalized semi-inner- product space. The notion of a generalized adjoint Abelian operator T on a Banach space X is introduced and shown that the null space N(T) is complemented; in fact \(X=N(T)\overline{\oplus R(T)}\). Finally, the countability of the point spectrum of an adjoint Abelian operator is obtained.