strongly continuous semigroup

strongly continuous semigroup

[¦strȯŋ·lē kən¦tin·yə·wəs ′sem·i‚grüp] (mathematics) A semigroup of bounded linear operators on a Banach space B, together with a bijective mapping T from the positive real numbers onto the semigroup, such that T (0) is the identity operator on B, T (s + t) = T (s) T (t) for any two positive numbers s and t and, for each element x of B, T (t) x is a continuous function of t.