In finite dimensional inner product (IP) spaces, any self-adjoint operator is normal and any normal operator is orthogonally diagonalizable.However, in semi-inner product (SIP) spaces, there exists an A-self-adjoint operator which is not A-normal.Therefore, it is interesting to study conditions for an A-self-adjoint operator on an SIP space to be A-orthogonally diagonalizable.An SIP is a mapping induced by a positive semi-definite operator on an IP space.In this paper, we study necessary, sufficient, and necessary and sufficient conditions for an A-self-adjoint operator to be A-orthogonally diagonalizable.
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Respitawulan et al. (2024) studied this question.
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