Gleason–Kahane–Żelazko Theorem for Bilinear Maps

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

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Bibliographische Detailangaben
Veröffentlicht in:	Annales mathematicae Silesianae 2022-09, Vol.36 (2), p.228-237
1. Verfasser:	Zivari-Kazempour, Abbas
Format:	Artikel
Sprache:	eng
Schlagworte:	46H25 46H99 47B48 bi-homomorphism bi-Jordan homomorphism Gleason–Kahane–Żelazko theorem preserves invertibility
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Beschreibung
Zusammenfassung:	Let and be two unital Banach algebras and U = × . We prove that the bilinear mapping : U → C is a bi-Jordan homomorphism if and only if is unital, invertibility preserving and jointly continuous. Additionally, if A is commutative, then is a bi-homomorphism.
ISSN:	2391-4238 2391-4238
DOI:	10.2478/amsil-2022-0017