Irreducible semigroups of functionally positive nilpotent operators
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- by Yong Zhong PDF
- Trans. Amer. Math. Soc. 347 (1995), 3093-3100 Request permission
Abstract:
For each irrational number $\theta \in (0,1)$, we construct a semigroup ${\mathcal {S}_\theta }$ of nilpotent operators on ${\mathcal {S}^2}([0,1])$ that are also partial isometries and positive in the sense that the operator maps nonnegative functions to nonnegative functions. We prove that each semigroup ${\mathcal {S}_\theta }$ is discrete in the norm topology and hence norm-closed and that the weak closure of ${\mathcal {S}_\theta }$ is independent of ${\mathcal {S}_\theta }$. We show that each semigroup ${\mathcal {S}_\theta }$ has no nontrivial invariant subspaces.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 347 (1995), 3093-3100
- MSC: Primary 47A15; Secondary 47B38, 47D03
- DOI: https://doi.org/10.1090/S0002-9947-1995-1264835-0
- MathSciNet review: 1264835