Asymptotic behavior and eigenvalues of dynamical semi-groups on operator algebras
β Scribed by Seiji Watanabe
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 704 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0022-247X
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π SIMILAR VOLUMES
Let \(\{T(t)\}_{1 \geqslant 0}\) be a \(C_{0}\)-semigroup in a Banach space \(X\) with generator \(A\). We prove that if \(\{T(t)\}_{t \geqslant 0}\) is bounded and sun-reflexive, and the sun-dual semigroup is not asymptotically stable, then there exist bounded complete trajectories under \(\{T(t)\}
In the present paper we consider the shift operator S on the Wiener algebra W (D) of analytic functions on the unit disc D of the complex plane C. A complex number Ξ» is called an extended eigenvalue of S if there exists a nonzero operator A satisfying the equation AS = Ξ»SA. We prove that the set of