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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Noncommuting unitary groups and local boundedness

Author: Jan Rusinek
Journal: Proc. Amer. Math. Soc. 101 (1987), 283-286
MSC: Primary 47D10; Secondary 47B25
MathSciNet review: 902542
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Abstract: We exhibit two unitary strongly continuous one-parameter groups $ {({e^{{A_1}t}})_{t \in {\mathbf{R}}}}$ and $ {({e^{{A_2}t}})_{t \in {\mathbf{R}}}}$ acting in a Hilbert space $ H$, a dense subspace $ D$ of $ H$ contained in the domains of $ {A_1}$ and $ {A_2}$ such that $ ({A_1}(D) \cup {A_2}(D)) \subset D$ and $ ({e^{{A_1}t}}(D) \cup {e^{{A_2}t}}(D)) \subset D$ for each $ t \in {\mathbf{R}}$, and an element $ x$ of $ D$ such that the function $ t \to \left\Vert {{A_1}{e^{{A_2}t}}x} \right\Vert$ is not locally bounded.

References [Enhancements On Off] (What's this?)

  • [1] P. E. T. Jørgensen and R. T. Moore, Operator commutation relations, commutation relations for operators, semigroups, and resolvents with applications to mathematical physics and representations of Lie groups, Reidel, Dordrecht, 1984.

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Article copyright: © Copyright 1987 American Mathematical Society