ArticleOriginal scientific text

Title

Concerning entire functions in B0-algebras

Authors 1

Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland

Abstract

We construct a non-m-convex non-commutative B0-algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.

Bibliography

  1. E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952).
  2. B. S. Mityagin, S. Rolewicz and W. Żelazko, Entire functions in B0-algebras, Studia Math. 21 (1962), 291-306.
  3. P. Turpin, Une remarque sur les algèbres à inverse continu, C. R. Acad. Sci. Paris 270 (1979), 1686-1689.
  4. L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Math. 230, Springer, 1971.
  5. W. Żelazko, Metric generalizations of Banach algebras, Rozprawy Mat. (Dissertationes Math.) 47 (1965).
  6. W. Żelazko, Selected Topics in Topological Algebras, Aarhus University Lecture Notes Ser. 31, 1971.
  7. W. Żelazko, A non-m-convex algebra on which operate all entire functions, Ann. Polon. Math. 46 (1985), 389-394.
  8. W. Żelazko, On certain open problems in topological algebras, Rend. Sem. Mat. Fis. Milano 59 (1989) (1992), 49-58.
Pages:
283-290
Main language of publication
English
Received
1994-01-27
Published
1994
Exact and natural sciences