Operator (quasi-)similarity, quasi-hermitian operators and all that
(2016) International Conference on Non-Hermitian Hamiltonians in Quantum Physics, PHHQP 201 — Location: Palermo, Italy (18.May.2015)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasisimilar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (pip-space), in particular the scale of Hilbert space s generated by a single unbounded metric operator.
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Antoine, J.-P., & Trapani, C. (2016). Operator (quasi-)similarity, quasi-hermitian operators and all that. Springer Proceedings in Physics, 184, 45-65. https://doi.org/10.1007/978-3-319-31356-6_4 (Original work published 2016)