Totally accretive operators
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- by Ralph deLaubenfels PDF
- Proc. Amer. Math. Soc. 103 (1988), 551-556 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 551-556
- MSC: Primary 47B44; Secondary 47D05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943083-7
- MathSciNet review: 943083