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On the equivalence of a theorem of Kisynski
and the Hille-Yosida generation theorem

Author: Wojciech Chojnacki
Journal: Proc. Amer. Math. Soc. 126 (1998), 491-497
MSC (1991): Primary 46J25; Secondary 43A20, 47A10, 47D03
MathSciNet review: 1415577
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Abstract: We show that a theorem of Kisynski on the generation of Banach-algebra homomorphisms of certain convolution algebras is equivalent to the Hille-Yosida theorem on the generation of operator-valued one-parameter semigroups.

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

  • 1. W. Arendt, Vector-valued Laplace transforms and Cauchy problems, Israel J. Math. 59 (1987), 327-352. MR 89a:47064
  • 2. H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach algebras, Ann. of Math. (2) 62 (1955), 217-229. MR 17:177a
  • 3. B. Hennig and F. Neubrander, On representations, inversions, and approximations of Laplace transforms in Banach spaces, Applicable Anal. 49 (1993), 151-170. MR 95m:46053
  • 4. J. Kisy\'{n}ski, personal communication.
  • 5. F. Neubrander, The Laplace-Stieltjes transform in Banach spaces and abstract Cauchy problems, Evolution equations, control theory, and biomathematics: proceedings of the Han-sur-Lesse conference (Ph. Clément and G. Lumer, eds.), Lecture Notes in Pure and Applied Mathematics, vol. 155, Marcel Dekker, Basel, 1994, pp. 417-431. MR 95d:47089
  • 6. K. Yosida, Functional Analysis, 5 ed., Springer-Verlag, Berlin, Heidelberg, New York, 1978. MR 58:17765

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Additional Information

Wojciech Chojnacki
Affiliation: Instytut Matematyki Stosowanej i Mechaniki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland; Department of Computer Science, University of Adelaide, Adelaide, SA 5005, Australia

Keywords: Banach algebra, convolution algebra, one-parameter semigroup, representation, resolvent
Received by editor(s): April 22, 1996
Received by editor(s) in revised form: August 12, 1996
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society

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