• Corpus ID: 246485570

Continuous bilinear maps on Banach $\star$-algebras

  title={Continuous bilinear maps on Banach \$\star\$-algebras},
  author={Behrooz Fadaee},
  • 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. 



Characterization of linear mappings on (Banach) ⋆-algebras by similar properties to derivations

Abstract Let 𝓐 be a ⋆-algebra, δ : 𝓐 → 𝓐 be a linear map, and z ∈ 𝓐 be fixed. We consider the condition that δ satisfies xδ(y)⋆ + δ(x)y⋆ = δ(z) (x⋆δ(y) + δ(x)⋆ y = δ(z)) whenever xy⋆ = z (x⋆ y =

Zero product determined matrix algebras

Zero product determined triangular algebras

Let 𝒜 be an algebra over a commutative unital ring 𝒞. We say that 𝒜 is zero product determined if for every 𝒞-module 𝒱 and every 𝒞-bilinear map φ: 𝒜 × 𝒜 → 𝒱 the following holds: if φ(A, B) =

Zero product determined some nest algebras

On bilinear maps determined by rank one idempotents

On derivations and Jordan derivations through zero products

Let $\A$ be a unital complex (Banach) algebra and $\M$ be a unital (Banach) $\A$-bimodule. The main results describe (continuous) derivations or Jordan derivations $D:\A\rightarrow \M$ through the

Linear maps on *-algebras acting on orthogonal elements like derivations or anti-derivations

Let U be a unital ?-algebra and δ : U → U be a linear map behaving like a derivation or an anti-derivation at the following orthogonality conditions on elements of U: xy = 0, xy? = 0, xy = yx = 0 and

Linear Maps on $$C^\star $$-Algebras Behaving like (Anti-)derivations at Orthogonal Elements

Let A be a \( C^\star \)-algebra, and let \(\delta :A \rightarrow A^{**}\) be a continuous linear map. We assume that \(\delta \) acts like a derivation or like an anti-derivation at orthogonal

Linear Maps on Standard Operator Algebras Characterized by Action on Zero Products

Let $${\mathcal {A}}$$A be a unital standard algebra on a complex Banach space $${\mathcal {X}}$$X with dim$${\mathcal {X}}\ge 2$$X≥2. The main result of this paper is to characterize the linear maps