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Previous $\lambda$-deformed {\it non-Hermitian} Hamiltonians with respect tothe usual scalar product of Hilbert spaces dealing with harmonicoscillator-like developments are (re)considered with respect to a new scalarproduct in order to take into account their property of self-adjointness. Thecorresponding deformed $\lambda$-states lead to new families of coherent statesaccording to the DOCS, AOCS and MUCS points of view.Comment: 10 page

NON-HERMITIAN OSCILLATOR-LIKE HAMILTONIANS AND λ-COHERENT STATES REVISITED