Category:Definitions/C0 Semigroups

This category contains definitions related to C0 Semigroups.
Related results can be found in Category:C0 Semigroups.

Let $\GF \in \set {\R, \C}$.

Let $X$ be a Banach space over $\GF$.

Let $\family {\map T t}_{t \ge 0}$ be a semigroup of bounded linear operators.

We say that $\family {\map T t}_{t \ge 0}$ is a $C_0$ semigroup if and only if:

$\ds \lim_{t \mathop \to 0^+} \map T t x = x$ for each $x \in X$.