Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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NON-LINEAR PRODUCT ℒℳ*-ℳℒ* ON PRIME *-ALGEBRAS

  • Mohd Arif Raza (Department of Mathematics, College of Science & Arts-Rabigh, King Abdulaziz University) ;
  • Tahani Al-Sobhi (Department of Mathematics, College of Science & Arts-Rabigh, King Abdulaziz University)
  • Received : 2023.03.21
  • Accepted : 2023.08.01
  • Published : 2023.09.30
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Abstract

In this paper, we explore the additivity of the map Ω : 𝒜 → 𝒜 that satisfies Ω([ℒ, ℳ]*)=[Ω (ℳ), ℒ]* + [ℳ, Ω(ℒ)]*, where [ℒ, ℳ]*= ℒℳ* - ℳ ℒ*, for all ℒ, ℳ ∈ 𝒜, a prime *-algebra with unit ℐ. Additionally we show that if Ω (αℐ) is self-adjoint operator for α ∈ {1, i} then Ω = 0.

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References

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