Abstract
We present conditions under which the Gel’fand transform \(E^{\wedge },\) of locally m-convex algebra E, is a dense subalgebra of \( \mathcal {C}_{c}(\mathfrak M(E))\). The partition of unity and the local theorem are given for a commutative unital locally m-convex algebra.
Similar content being viewed by others
References
Arens, R.: The problem of locally-A functions in a commutative Banach algebra A. Trans. Am. Math. Soc. 104, 24–36 (1962)
Brooks, R.M.: Partitions of unity in F-algebras. Math. Ann. 77, 265–272 (1968)
Gel’fand, I., Raikov, D., Shilov, G.: Commutative Normed Rings. Chelsea, New York (1964)
Haag, R.: Local Quantum Physics. Fields, Particles, Algebras, 2nd edn. Springer, Berlin (1996)
Mallios, A.: Topological Algebras. Selected Topics. North-Holland, Amsterdam (1986)
Mallios, A.: On geometric topological algebras. J. Math. Anal. Appl. 172, 301–322 (1993)
Mallios, A.: Geometry of Vector Sheaves. An Axiomatic Approach to Differential Geometry, vol. 1–2. Kluwer Acad. Publ., Dordrecht (1998)
Mallios, A.: On localising topological algebras. Contemp. Math. 341, Amer. Math. Soc. Providence, RI, pp. 79–95 (2004)
Mallios, A., Oukhouya, A.: k-algèbres topologiques. Sci. Math. Jpn 61, 105–110 (2005)
Mallios, A., Oukhouya, A.: On combinatorially regular topological algebra. Contemp. Math. 427, Amer. Math. Soc. Providence, RI, pp. 285–290 (2007)
Oukhouya, A.: On local topological algebras. Sci. Math. Jpn. 57, 493–497 (2003). ([elect. version: e7, 277-281])
A. Oukhouya, On combinatorially regular Fréchet algebra. Contemp. Math. 427, Amer. Math. Soc. Providence, RI, pp. 339–344 (2007)
Fragoulopoulou, M.: Topological Algebras with Involution. Elsevier, Amsterdam (2005)
Nachbin, L.: Elements of Approximation Theory. D. van Nostrand, Princeton, NJ (1967)
Pal, M.: Advanced Algebra. Delhi (2013)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of author, there is no conflict of interest.
Additional information
Communicated by Mohammad Reza Koushesh.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Oukhouya, A. On the Gel’fand Theory for Topological Algebras. Bull. Iran. Math. Soc. 50, 26 (2024). https://doi.org/10.1007/s41980-023-00854-9
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s41980-023-00854-9