Abstract
Motivated by the recent developments of pseudo-Hermitian quantummechanics, we analyze the structure of unbounded metric operators in a Hilbertspace. It turns out that such operators generate a canonical lattice of Hilbertspaces, that is, the simplest case of a partial inner product space (PIP-space).Next, we introduce several generalizations of the notion of similarity betweenoperators and explore to what extent they preserve spectral properties. Then weapply some of the previous results to operators on a particular PIP-space, namelya scale of Hilbert spaces generated by ametric operator. Finally, we reformulatethe notion of pseudo-Hermitian operators in the preceding formalism.
Lingua originale | English |
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Numero di pagine | 21 |
Rivista | JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL |
Volume | 46 |
Stato di pubblicazione | Published - 2013 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)