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 \(\mathrm{A}\) 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

Metrics Loading ...

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
Scopus
Google Scholar
Europe PMC