Representation of non-semibounded quadratic forms and orthogonal additivity
| Autor: | Ibort, Alberto, Llavona, José G., Lledó, Fernando, Pérez-Pardo, Juan Manuel |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Journal of Mathematical Analysis and Applications 495 (2021) 124783 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmaa.2020.124783 |
| Popis: | A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of the underlying Hilbert space and orthogonal additivity. We apply this result to several examples, including the position operator in quantum mechanics and quadratic forms invariant under a unitary representation of a separable locally compact group. The case of invariance under a compact group is also discussed in detail. Comment: Substantial changes with respect to v1. Introduction of the notion of strong representability and substantial simplification of the proofs in Section 4. To appear in J. Math. Anal. Appl |
| Databáze: | arXiv |
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