Strong stability is the property of a strongly continuous semigroup 
on a Banach space 
such that
 |
for every 
.
This is pointwise convergence on vectors
and need not imply convergence of 
in the operator norm.
The stronger condition of exponential stability
implies strong stability, but the converse need not hold. The Arendt-Batty-Lyubich-Vũ
theorem gives conditions involving the operator
spectrum that imply strong stability.
