I was wondering if there is some relaxation of the configuration (or phase) space when considering pseudo-Hermitian physical situations vs Hermitian? For instance in "$C^*$-Algebras of Energy Observables: I. General Theory and Bumps Algebras" the authors (GEORGESCU and IFTIMOVICI) let the configuration space be an arbitrary abelian locally compact group X. Are there any relaxations here when we look at pseudo-Hermitian Hamiltonians? Or just in general if/can the configuration space (or phase space) change in pseudo-Hermitian vs Hermitian QM?
