Abstract
Let $T(\cdot)$ be a bounded $C_0$-semigroup on the Banach space $X$, with generator $A$. It is shown that the denseness of range $A$ is necessary and sufficient for the semigroup's mean stability with respect to suitable weights. Analogous results are valid for power bounded operators, tensor product semigroups, and cosine operator functions.
Citation
Shmuel Kantorovitz. Serguei Piskarev. "MEAN STABILITY OF SEMIGROUPS." Taiwanese J. Math. 6 (1) 89 - 103, 2002. https://doi.org/10.11650/twjm/1500407402
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