On the quasi-central elements of Banach algebras

Downloads

DOI:

https://doi.org/10.26637/MJM0803/0047

Abstract

In the eighties of the last century Rennison studied and characterized the set of quasi-central elements of some unital Banach algebras. In this paper, we improve one of Rennison's result assert that for given unital Banach algebra A the set of quasi-central elements Q(A), need not be equal to centre of A and need not be closed under addition or multiplication. Further, we prove that if A is unital ultraprime Banach algebra, then Q(A) need not be equal to centre of A and need not be closed under addition or multiplication.

Keywords:

quasi-central elements, ultraprime algebra

Mathematics Subject Classification:

Mathematics
  • Ekram M. Abdullah Department of Mathematics, College of Education for Pure Sciences, University of Mosul, Mosul, Iraq.
  • Amir A. Mohammed Department of Mathematics, College of Education for Pure Sciences, University of Mosul, Mosul, Iraq.
  • Pages: 1007-1011
  • Date Published: 01-07-2020
  • Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

J. F. Rennison, The quasi-centre of a Banach algebra, Math Proc. Campridge Philos. Soc., 103(1988), 333-337.

M. Mathieu, The symmetric algebra of quotients of an ultraprime Banach algebra, J. Austral. Math. Soc. Ser. A., 50(1)(1991), 75-87.

J. F. Rennison, Conditions related to centrality in a Banach algebra, J. London Math. Soc., 26(2)(1982), 155168.

J. F. Rennison, Conditions related to centrality in a Banach algebra II, J. London Math. Soc., 35(2)(1987), 499513.

C. Le Page, Sur quelques conditions entrainant la commutative dans les algebres, Banach. C. R. Acad. Sci. Paris Ser. $A-B, 265(1967), 235-237$.

A. A. Mohammed, On ultrasemiprime algebras, Dirasat, Pure Sciences, 33(1)(2006), 82-84.

J. F. Rennison. Closure properties of the quasi-centre of a Banach algebra, Math Proc. Campridge Philos. Soc., 108(1990), 355-364.

A.Y. Asad, Extended centrality in a complex Banach algebra, International Mathematical Forum, 13(3)(2018),

  • NA

Metrics

PDF views
27
Jul 2020Jan 2021Jul 2021Jan 2022Jul 2022Jan 2023Jul 2023Jan 2024Jul 2024Jan 2025Jul 2025Jan 20265.0
|

Published

01-07-2020

How to Cite

Ekram M. Abdullah, and Amir A. Mohammed. “On the Quasi-Central Elements of Banach Algebras”. Malaya Journal of Matematik, vol. 8, no. 03, July 2020, pp. 1007-11, doi:10.26637/MJM0803/0047.

Issue

Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

Section

Articles

License

Copyright (c) 2020 MJM

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
0
Scopus
Google Scholar
Europe PMC