ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
cover
Proceedings of the Estonian Academy of Sciences. Physics. Mathematics

Galbed algebras and their sectional representation; pp. 3–16

Full article in PDF format | 10.3176/phys.math.2007.1.01

Authors
Mart Abel, Veiko Lehto

Abstract

In this paper we prove that the unitization A×K of a topological algebra A is αn-galbed if and only if A is αn-galbed. We also find sufficient conditions under which a unital strongly galbed algebra can be represented as a subalgebra of some section algebra.


References

1. Turpin, Ph. Généralisations d’un théorème de S. Mazur et W. Orlicz. C. R. Acad. Sci. Paris, 1971, 273, 457–460.

2. Turpin, Ph. Variantes de résultats de S. Mazur et W. Orlicz. C. R. Acad. Sci. Paris, 1971, 273, 506–509.

3. Turpin, Ph. Espaces et intersections d’espaces d’Orlicz non localement convexes. Studia Math., 1973, 46, 167–195.
https://doi.org/10.4064/sm-46-2-167-195

4. Turpin, Ph. Espaces et opérateurs exponentiellement galbés. In Seminaire Pierre Lelong (Analyse) Année 1973/74 (Lelong, P., ed.), Lecture Notes in Math., 1975, 474, 48–62.
https://doi.org/10.1007/BFb0077398

5. Turpin, Ph. Convexités dans les espaces vectoriels topologiques généraux. Dissertationes Math. (Rozprawy Mat.), 131, PWN, Warszawa, 1976.

6. Abel, Mart. Structure of Gelfand–Mazur Algebras. Dissertationes Mathematicae Universitatis Tartuensis, 31, Tartu University Press, Tartu, 2003.

7. Abel, Mart. The center of topologically primitive galbed algebras. In Topological Algebras, Their Applications and Related Topics (Jarosz, K. and Sołtysiak, A., eds), Banach Center Publ., 2005, 67, 45–54.
https://doi.org/10.4064/bc67-0-4

8. Abel, Mart. On the center of galbed algebras. Bull. Greek Math. Soc. (to appear).

9. Abel, Mart and Abel, Mati. The center of topologically primitive exponentially galbed algebras. Int. J. Math. Math. Sci., 2006, Art. ID 19697, 1–10.
https://doi.org/10.1155/IJMMS/2006/19697

10. Abel, Mart and Abel, Mati. On galbed algebras and galbed spaces (to appear).

11. Abel, Mati. On the Gelfand–Mazur theorem for exponentially galbed algebras. Tartu Ülik. Toimetised, 1990, 899, 65–70.

12. Abel, Mati. Galbed Gelfand–Mazur algebras. In Topological Algebras and Their Applications (Arizmendi, H., Bosch, C. and Palacios, L., eds), Contemp. Math., 2004, 341, 17–24.
https://doi.org/10.1090/conm/341/06159

13. Lehto, V. Galbed Algebras and Their Sectional Representation. Bachelor’s Thesis, Tartu, 2006 (in Estonian).

14. Allan, G. R. A spectral theory for locally convex algebras. Proc. London Math. Soc., 1965, 15, 399–421.
https://doi.org/10.1112/plms/s3-15.1.399

15. Bonsall, F. F. and Duncan, J. Complete normed algebras. Ergeb. Math. Grenzgeb., 1973, 80.
https://doi.org/10.1007/978-3-642-65669-9

16. Horváth, J. Topological Vector Spaces and Distributions I. Addison-Wesley Publ. Co., Reading, Mass.-London- Don Mills, Ont., 1966.


Back to Issue