On the quasi-central elements of Banach algebras

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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)

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

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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.