|
On the equivalence of a theorem of Kisynski and the Hille-Yosida generation theorem
Author(s):
Wojciech
Chojnacki
Journal:
Proc. Amer. Math. Soc.
126
(1998),
491-497.
MSC (1991):
Primary 46J25;
Secondary 43A20, 47A10, 47D03
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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:
- 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
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
46J25,
43A20, 47A10, 47D03
Retrieve articles in all Journals with MSC
(1991):
46J25,
43A20, 47A10, 47D03
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
Email:
wojtekch@appli.mimuw.edu.pl, wojtek@cs.adelaide.edu.au
DOI:
10.1090/S0002-9939-98-04048-9
PII:
S 0002-9939(98)04048-9
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
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org