Representations of correlations of the $і [A, B] = f(A) + g(B)$ type
It is proved that all nontrivial representations of quadratic relation $i [A, B] = f(A) + g(B)$ with self-adjoint operators $A, B$ are unbounded if $f$ and $g$ are nonnegative; for any $f$ and $g$ this relation does not have nontrivial finite-dimensional representations and factor-representations of...
Збережено в:
| Дата: | 1991 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Російська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1991
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9313 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | It is proved that all nontrivial representations of quadratic relation $i [A, B] = f(A) + g(B)$ with self-adjoint operators $A, B$ are unbounded if $f$ and $g$ are nonnegative; for any $f$ and $g$ this relation does not have nontrivial finite-dimensional representations and factor-representations of type $II_I$, but can have infinite-dimensional irreducible representations with bounded operators. |
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