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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A note on generators of semigroups


Author: Sze Kai Tsui
Journal: Proc. Amer. Math. Soc. 66 (1977), 305-308
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1977-0454654-1
MathSciNet review: 0454654
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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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Keywords: Semigroups of contractions, infinitesimal generators, spatial numerical range, numerical range, dissipative operators, <IMG WIDTH="31" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${C^\ast }$">-algebras, positive linear mappings
Article copyright: © Copyright 1977 American Mathematical Society