<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Let <italic>A</italic> and <italic>B</italic> be two unital Banach algebras and 𝔘 = <italic>A</italic> × <italic>B</italic>. We prove that the bilinear mapping <italic>φ</italic>: 𝔘 → ℂ is a bi-Jordan homomorphism if and only if <italic>φ</italic> is unital, invertibility preserving and jointly continuous. Additionally, if A is commutative, then <italic>φ</italic> is a bi-homomorphism.</p>
</abstract>

Let A and B be two unital Banach algebras and 𝔘 = A × B. We prove that the bilinear mapping φ: 𝔘 → ℂ is a bi-Jordan homomorphism if and only if φ is unital, invertibility preserving and jointly continuous. Additionally, if A is commutative, then φ is a bi-homomorphism.

Gleason–Kahane–Żelazko Theorem for Bilinear Maps

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Gleason\u2013Kahane\u2013Żelazko Theorem for Bilinear Maps"}

Let A and B be two unital Banach algebras and 𝔘 = A × B. We prove that the bilinear mapping φ: 𝔘 → ℂ is a bi-Jordan homomorphism if and only if φ is unital,...

Gleason–Kahane–Żelazko Theorem for Bilinear Maps

Published Online: Sep 15, 2022

Page range: 228 - 237

Received: Sep 09, 2021

Accepted: Aug 31, 2022

DOI: https://doi.org/10.2478/amsil-2022-0017

Keywords
Gleason–Kahane–Żelazko theorem, preserves invertibility, bi-homomorphism, bi-Jordan homomorphism

© 2022 Abbas Zivari-Kazempour, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Gleason–Kahane–Żelazko Theorem for Bilinear Maps

Published Online: Sep 15, 2022

Page range: 228 - 237

Received: Sep 09, 2021

Accepted: Aug 31, 2022

DOI: https://doi.org/10.2478/amsil-2022-0017

KeywordsGleason–Kahane–Żelazko theorem, preserves invertibility, bi-homomorphism, bi-Jordan homomorphism

© 2022 Abbas Zivari-Kazempour, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Gleason–Kahane–Żelazko theorem, preserves invertibility, bi-homomorphism, bi-Jordan homomorphism