Timeline for Spectral theorem for commuting operators
Current License: CC BY-SA 4.0
5 events
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| Jul 6, 2023 at 14:02 | comment | added | MaoWao | Yes, commutation of the projection valued-measures or equivalently all bounded Borel functions of the operators. These kind of issues are carefully discussed in Schmüdgen's book on Unbounded Self-Adjoint Operators on Hilbert spaces. | |
| Jul 5, 2023 at 15:08 | comment | added | JustWannaKnow | @MaoWao thanks for the comment. I fixed the wrong sign in the commutation relation. You actually solved one of my questions: it is not clear by the authors presentation what they mean by commutation relations, since they only mention the term. You mean commutation relation in the strong sense = commutation of all its projection valued measures? | |
| Jul 5, 2023 at 15:04 | history | edited | JustWannaKnow | CC BY-SA 4.0 |
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| Jul 5, 2023 at 14:51 | comment | added | MaoWao | Your formulation of the spectral theorem for commuting self-adjoint operators is not correct. What you need is that the operators commute strongly, which is stronger than commutation on a common dense subspace (or even common core for the operators). And it should be commutation, not anti-commutation anyway. | |
| Jul 5, 2023 at 14:22 | history | asked | JustWannaKnow | CC BY-SA 4.0 |