## Riesz decomposition property implies asymptotic periodicity of positive and constrictive operators

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- by Wojciech Bartoszek PDF
- Proc. Amer. Math. Soc.
**116**(1992), 101-111 Request permission

## Abstract:

Consider a linear and positive operator ${\mathbf {T}}$ acting on an ordered, $F$-normed linear space ${\mathbf {X}}$. Assume that there exists an open neighborhood ${\mathbf {U}} \ni {\mathbf {0}}$ such that the trajectory $\left \{ {{{\mathbf {T}}^n}({\mathbf {x}})} \right \}$ is attracted to a compact set ${{\mathbf {F}}_{\mathbf {U}}}$ whenever ${\mathbf {x}}$ is taken from ${\mathbf {U}}$ and that the positive cone ${{\mathbf {X}}_ + }$ is closed, proper, and reproducing. It is shown that if $({\mathbf {X}},{{\mathbf {X}}_ + })$ has the Riesz Decomposition Property then ${\mathbf {T}}$ has asymptotically periodic iterates.## References

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## Additional Information

- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**116**(1992), 101-111 - MSC: Primary 47B65; Secondary 46B40, 47A35, 47B60
- DOI: https://doi.org/10.1090/S0002-9939-1992-1123648-3
- MathSciNet review: 1123648