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# Totally Accretive Operators

Ralph Delaubenfels
Proceedings of the American Mathematical Society
Vol. 103, No. 2 (Jun., 1988), pp. 551-556
DOI: 10.2307/2047178
Stable URL: http://www.jstor.org/stable/2047178
Page Count: 6
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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 $\{e^{-tA} \}_{t \geq 0}$, 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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