Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] A. Beurling, Sur les intégrales de Fourier absolument convergentes et leur application à une transformation fonctionnelle, Neuvième Congrès Math. Scandinaves (Helsinki, 1938), Tryekeri, Helsinki, 1939, pp. 199-210.
  • [2] Ralph Philip Boas Jr., Entire functions, Academic Press Inc., New York, 1954. MR 0068627
  • [3] H. G. Dales and W. K. Hayman, Esterle’s proof of the Tauberian theorem for Beurling algebras, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 4, vi, 141–150 (English, with French summary). MR 644346
  • [4] Jean Esterle, A complex-variable proof of the Wiener Tauberian theorem, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 2, vii, 91–96 (English, with French summary). MR 584273
  • [5] A. Hulanicki, Subalgebra of 𝐿₁(𝐺) associated with Laplacian on a Lie group, Colloq. Math. 31 (1974), 259–287. MR 0372536, https://doi.org/10.4064/cm-31-2-259-287
  • [6] -, private communication.
  • [7] Horst Leptin, Ideal theory in group algebras of locally compact groups, Invent. Math. 31 (1975/76), no. 3, 259–278. MR 0399344, https://doi.org/10.1007/BF01403147
  • [8] Allan M. Sinclair, Continuous semigroups in Banach algebras, London Mathematical Society Lecture Note Series, vol. 63, Cambridge University Press, Cambridge-New York, 1982. MR 664431

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J05, 47D05

Retrieve articles in all journals with MSC: 46J05, 47D05


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

American Mathematical Society