Gleason–Kahane–Żelazko Theorem for Bilinear Maps

Abbas Zivari-Kazempour

doi:10.2478/amsil-2022-0017

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Gleason–Kahane–Żelazko Theorem for Bilinear Maps

Annales Mathematicae Silesianae

Volume 36 (2022): Issue 2 (September 2022)

By: Abbas Zivari-Kazempour

Open Access

|Sep 2022

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.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2022-0017 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 228 - 237

Submitted on: Sep 9, 2021

Accepted on: Aug 31, 2022

Published on: Sep 15, 2022

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Gleason–Kahane–Żelazko theorem,

preserves invertibility,

bi-homomorphism,

bi-Jordan homomorphism

Related subjects:

Mathematics,

General mathematics

© 2022 Abbas Zivari-Kazempour, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 36 (2022): Issue 2 (September 2022)