New Condition of Automatic Continuity of Dense Range Homomorphisms on Jordan – Banach Algebras

Balo, Ruqayah N.; Abdulrazaq, Nadia A.; Abdullah, Duaa F.

doi:10.33899/edusj.2018.159292

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2022

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“…Since T is a dense range Jordan homomorphism, we have r Γ + (T a) ≤ r Λ + (a), ∀a ∈ Λ + . This Corollary 3.4 is a generalization of Theorem 2.2 in[3].4. conclusionWe extended the open Problem 1.7 in Banach algebras to Jordan Banach algebras as an open Problem 2.4 to every dense range Jordan almost multiplicative map from a Jordan Banach algebra to a semisimple Jordan Banach algebra for automatic continuity.…”

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confidence: 58%

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Automatic continuity of Jordan almost multiplicative maps on special Jordan Banach algebras

2022

Eur. J. Math. Appl.

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If T : Λ → Γ is a dense range homomorphism from a Banach algebra Λ to a semisimple Banach algebra Γ, then the automatic continuity of T is being a long-standing open question. The concept of Jordan almost multiplicative maps between Jordan Banach algebras is introduced, and an extension of this open question to Jordan Banach algebras is considered. Also, a partial answer to the extended open question is derived in the sense that every dense range Jordan almost multiplicative map T from a special Jordan Banach algebra Λ + to a semisimple special Jordan Banach algebra Γ + , with an additional condition on Λ + and Γ + , is continuous.

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confidence: 58%

“…Here the Jordan product is distributive over addition. There are many articles for automatic continuity in Jordan Banach algebras, see for example [1][2][3]23].…”

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confidence: 99%

Automatic continuity of Jordan almost multiplicative maps on special Jordan Banach algebras

2022

Eur. J. Math. Appl.

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show abstract

New Condition of Automatic Continuity of Dense Range Homomorphisms on Jordan – Banach Algebras

Cited by 1 publication

References 4 publications

Automatic continuity of Jordan almost multiplicative maps on special Jordan Banach algebras

Automatic continuity of Jordan almost multiplicative maps on special Jordan Banach algebras

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