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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A converse of Lotz's theorem on uniformly continuous semigroups


Author: J. M. A. M. van Neerven
Journal: Proc. Amer. Math. Soc. 116 (1992), 525-527
MSC: Primary 47D03; Secondary 46B20, 47B38
MathSciNet review: 1097355
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Abstract: We prove the following partial converse to a theorem of Lotz: If every $ {C_0}$-semigroup on a Banach lattice $ E$ with quasi-interior point is uniformly continuous, then $ E$ is isomorphic to a $ C(K)$-space with the Grothendieck property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1097355-X
PII: S 0002-9939(1992)1097355-X
Keywords: Strongly continuous semigroups, Grothendieck property, Dunford-Pettis property, Banach lattice with quasi-interior point
Article copyright: © Copyright 1992 American Mathematical Society