# Continuous bilinear maps on Banach $\star$-algebras

@inproceedings{Fadaee2022ContinuousBM, title={Continuous bilinear maps on Banach \$\star\$-algebras}, author={Behrooz Fadaee}, year={2022} }

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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