Totally accretive operators

Author:
Ralph deLaubenfels

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

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Abstract: Let be a (possibly unbounded) linear operator on a Banach space. We show that, when generates a uniformly bounded strongly continuous semigroup , then generates a bounded holomorphic semigroup (BHS) of angle if and only if generates a BHS of angle . We show that each power of generates a uniformly bounded strongly continuous semigroup if and only if generates a BHS of angle if and only if each power of generates a BHS of angle . If is a linear operator on a Hilbert space, then each power of generates a strongly continuous contraction semigroup if and only if is positive selfadjoint.

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DOI:
https://doi.org/10.1090/S0002-9939-1988-0943083-7

Article copyright:
© Copyright 1988
American Mathematical Society