• Corpus ID: 246485570

Continuous bilinear maps on Banach $\star$-algebras

@inproceedings{Fadaee2022ContinuousBM,
  title={Continuous bilinear maps on Banach \$\star\$-algebras},
  author={Behrooz Fadaee},
  year={2022}
}
  • B. Fadaee
  • Published 3 February 2022
  • Mathematics
Let A be a unital Banach ⋆-algebra with unity 1, X be a Banach space and φ : A× A → X be a continuous bilinear map. We characterize the structure of φ where it satisfies any of the following properties: a, b ∈ A, ab⋆ = z (a⋆b = z) ⇒ φ(a, b⋆) = φ(z, 1) (φ(a⋆ , b) = φ(z, 1)); a, b ∈ A, ab⋆ = z (a⋆b = z) ⇒ φ(a, b⋆) = φ(1, z) (φ(a⋆ , b) = φ(1, z)), where z ∈ A is fixed. 

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