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Regularity of Banach algebras generated by analytic semigroups satisfying some growth conditions


Authors: J. Esterle and J. E. Galé
Journal: Proc. Amer. Math. Soc. 92 (1984), 377-380
MSC: Primary 46J05; Secondary 47D05
DOI: https://doi.org/10.1090/S0002-9939-1984-0759656-7
MathSciNet review: 759656
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Abstract: We show that if a commutative complex Banach algebra $ A$ is generated by a nonzero analytic semigroup $ ({a^t})\operatorname{Re} t > 0$ satisfying

$\displaystyle \int {\begin{array}{*{20}{c}} { + \infty } \\ { - \infty } \\ \en... ...{\log }^ + }\left\Vert {{a^{1 + it}}} \right\Vert}}{{1 + {t^2}}}dt < + \infty ,$

, then $ A$ is regular in Shilov's sense.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0759656-7
Keywords: Regular Banach algebra, analytic semigroup
Article copyright: © Copyright 1984 American Mathematical Society

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