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|Title||Some Remarks of Centrality in a Nonunital Complex Banach Algebra.|
We show under certain condition that the set of all ρ-quasi central elements of a nonunital complex Banach algebra A is a subset of the set of all ρ-quasi central elements of A*, the unitization of A. Also we show under certain condition, the set of all ρ-quasi, the set of all σ-quasi and the set of all quasi centralizer elements of a subalgebra B of a complex Banach algebra A are subsets of the set of all ρ-quasi, all σ-quasi and all quasi centralizer elements of B*, respectively. Finally we prove that under certain condition the ρ-quasi, the σ-quasi and the quasi centralizer are preserved under the quotient mapping. Some previous results of Renneson and As' ad obtained in 1982 and 1999, respectively are generalized.
|Published in||Southeast Asian Bulletin of Mathematics|
|Series||Volume: 30, Number: 6|
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