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Is weak pseudo-Hermiticity weaker than pseudo-Hermiticity?

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For 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.

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American Institute of Physics (AIP) Publishing

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Mathematical physics

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Journal of Mathematical Physics

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10.1063/1.2338144

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