Abstract
Let T(·) be a bounded C0-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.
Original language | English |
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Pages (from-to) | 89-103 |
Number of pages | 15 |
Journal | Taiwanese Journal of Mathematics |
Volume | 6 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2002 |
Keywords
- C-semigroup
- Cosine operator function
- Generator
- Mean stability
- Point spectrum
- Power bounded operator
- Residual spectrum
- Semigroup
- Tensor product of semigroups