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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, Number 4, Pages 3–10
(Mi ivm8883)
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This article is cited in 1 scientific paper (total in 1 paper)
One classification of von Neumann algebra in a space with conjugation
E. V. Vladovaa, M. S. Matveichukb, Yu. G. Ogaic a Chair of Higher Mathematics, Ul'yanovsk State Pedagogical University, 4 100-letiya Oktyabrya Sq., Ul'yanovsk, 432700 Russia
b Chair of Higher Mathematics, Kazan National Research Technical University, 10 K. Marksa str., Kazan, 420111 Russia
c Ul'yanovsk State Pedagogical University, 4 100-letiya Oktyabrya Sq., Ul'yanovsk, 432700 Russia
Abstract:
In this paper for the first time we show that in the complex Hilbert space with the conjugation operator a classification of von Neumann algebras is possible. Similar classification is known for Krein spaces. Projectors (idempotents) often serve as elements of quantum logic. In operator theories projectors play the role of elements from which bounded operators are constructed. For one special case we show that for any projector from von Neumann algebra which acts in a separable Hilbert space one can always find conjugation operator $J$ adjoined to this algebra for which the projector is self-adjoint.
Keywords:
Hilbert space, von Neumann algebra, conjugation operator, projection.
Received: 31.10.2012
Citation:
E. V. Vladova, M. S. Matveichuk, Yu. G. Ogai, “One classification of von Neumann algebra in a space with conjugation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 4, 3–10; Russian Math. (Iz. VUZ), 58:4 (2014), 1–6
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https://www.mathnet.ru/eng/ivm8883 https://www.mathnet.ru/eng/ivm/y2014/i4/p3
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Abstract page: | 149 | Full-text PDF : | 36 | References: | 30 | First page: | 1 |
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