Center and Quasi Center on Banach Normal Hyperalgebra


Article info

2021-08-26
2021-12-28
75 - 90

Keywords

  • quasi-center
  • Banach hyperalgbera
  • center
  • normal hyperalgebra
  • Hahn Banach Theorem

Abstract

In this paper, we prove that every strongly distributive hyperalgebra is normal. Also, we prove that if X is a normed normal hyperalgebra with a propertyza◦x.zb◦y = zab◦xy and |λ| > ‖x‖, then (zλ◦e − x) is invertible. Moreover, we give a characterization of the center of a unital complex Banach normal hyperalgebra with the same property. Finally, we define the quasi-center, σ-quasi center and ρ-quasi center of Banach normal hyperalgebra as a generalization of the center and study some basic properties and relations between them.

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Center and Quasi Center on Banach Normal Hyperalgebra


معلومات المقال

2021-08-26
2021-12-28
75 - 90

الكلمات الإفتتاحية

  • quasi-center
  • Banach hyperalgbera
  • center
  • normal hyperalgebra
  • Hahn Banach Theorem

الملخص

In this paper, we prove that every strongly distributive hyperalgebra is normal. Also, we prove that if X is a normed normal hyperalgebra with a propertyza◦x.zb◦y = zab◦xy and |λ| > ‖x‖, then (zλ◦e − x) is invertible. Moreover, we give a characterization of the center of a unital complex Banach normal hyperalgebra with the same property. Finally, we define the quasi-center, σ-quasi center and ρ-quasi center of Banach normal hyperalgebra as a generalization of the center and study some basic properties and relations between them.

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