## Taiwanese Journal of Mathematics

### MEAN STABILITY OF SEMIGROUPS

#### 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.

#### Article information

Source
Taiwanese J. Math., Volume 6, Number 1 (2002), 89-103.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407402

Digital Object Identifier
doi:10.11650/twjm/1500407402

Mathematical Reviews number (MathSciNet)
MR1884457

Zentralblatt MATH identifier
1041.47021

#### Citation

Kantorovitz, Shmuel; Piskarev, Serguei. MEAN STABILITY OF SEMIGROUPS. Taiwanese J. Math. 6 (2002), no. 1, 89--103. doi:10.11650/twjm/1500407402. https://projecteuclid.org/euclid.twjm/1500407402