Department of Mathematics2024-11-0920060022-248810.1063/1.23381442-s2.0-33749349010https://hdl.handle.net/20.500.14288/2795For a weakly pseudo-Hermitian linear operator, we give a spectral condition that ensures its pseudo-Hermiticity. This condition is always satisfied whenever the operator acts in a finite-dimensional Hilbert space. Hence weak pseudo-Hermiticity and pseudo-Hermiticity are equivalent in finite-dimensions. This equivalence extends to a much larger class of operators. Quantum systems whose Hamiltonian is selected from among these operators correspond to pseudo-Hermitian quantum systems possessing certain symmetries.pdfMathematical physicsJournal Article1089-7658https://doi.org/10.1063/1.2338144240877500001Q3NOIR00569