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

 

Totally accretive operators


Author: Ralph deLaubenfels
Journal: Proc. Amer. Math. Soc. 103 (1988), 551-556
MSC: Primary 47B44; Secondary 47D05
MathSciNet review: 943083
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Abstract: Let $ A$ be a (possibly unbounded) linear operator on a Banach space. We show that, when $ A$ generates a uniformly bounded strongly continuous semigroup $ {\left\{ {{e^{ - tA}}} \right\}_{t \geq 0}}$, then $ {A^2}$ generates a bounded holomorphic semigroup (BHS) of angle $ \theta $ if and only if $ A$ generates a BHS of angle $ \theta / 2 + \pi / 4$. We show that each power of $ A$ generates a uniformly bounded strongly continuous semigroup if and only if $ A$ generates a BHS of angle $ \pi / 2$ if and only if each power of $ A$ generates a BHS of angle $ \pi / 2$. If $ A$ is a linear operator on a Hilbert space, then each power of $ A$ generates a strongly continuous contraction semigroup if and only if $ A$ is positive selfadjoint.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0943083-7
PII: S 0002-9939(1988)0943083-7
Article copyright: © Copyright 1988 American Mathematical Society