On the Birman–Krein Theorem
It is shown that if $X$ is a unitary operator so that a singular subspace of $U$ is unitarily equivalent to a singular subspace of $UX$ (or $XU$), for each unitary operator $U$, then $X$ is the identity operator. In other words, there is no nontrivial generalization of Birman–Krein Theorem that incl...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.473/ |