A note on generators of semigroups

Tsui, Sze Kai

doi:10.1090/S0002-9939-1977-0454654-1

A note on generators of semigroups
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Proc. Amer. Math. Soc. 66 (1977), 305-308 Request permission

Abstract:

The generator T of a norm-continuous semigroup of identity preserving positive linear mappings on a ${C^\ast }$-algebra $\mathfrak {A}$ is characterized as one that satisfies $T({u^\ast }u) \geqslant {u^\ast }T(u) + T({u^\ast })u$ for all unitary elements u in $\mathfrak {A}$.

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