Jean-Pierre Antoine, Camillo Trapani
Published 2015-10-09Version 1
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 quasi-similar 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), in particular the scale of Hilbert spaces generated by a single unbounded metric operator.
Comments: 16 pages. arXiv admin note: text overlap with arXiv:1409.3497, arXiv:1210.3163, arXiv:1307.5644
Partial inner product spaces, metric operators and generalized hermiticity
Spinors in $\mathbb{K}$-Hilbert Spaces
Symmetries of finite Heisenberg groups for multipartite systems
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