6533b85afe1ef96bd12b8e0c
RESEARCH PRODUCT
Partial inner product spaces, metric operators and generalized hermiticity
Jean-pierre AntoineCamillo Trapanisubject
Statistics and ProbabilityPure mathematicsQuantum PhysicsSpectral propertiesHilbert spaceFOS: Physical sciencesGeneral Physics and Astronomymetric operatorStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Formalism (philosophy of mathematics)symbols.namesakeInner product spaceOperator (computer programming)pip-spacesSettore MAT/05 - Analisi MatematicaModeling and SimulationLattice (order)symbolsgeneralized hermiticityQuantum Physics (quant-ph)Mathematical PhysicsMathematicsdescription
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is, the simplest case of a partial inner product space (PIP space). Next, we introduce several generalizations of the notion of similarity between operators and explore to what extend they preserve spectral properties. Then we apply some of the previous results to operators on a particular PIP space, namely, a scale of Hilbert spaces generated by a metric operator. Finally, we reformulate the notion of pseudo-hermitian operators in the preceding formalism.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-01-01 |