双线性映射的Gleason–Kahane–Żelazko定理

IF 0.4 Q4 MATHEMATICS

Annales Mathematicae Silesianae Pub Date : 2022-09-01 DOI:10.2478/amsil-2022-0017

A. Zivari-kazempour

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引用次数: 0

摘要

摘要设A和B是两个一元Banach代数，且𝔘= A × B，证明了双线性映射φ:𝔘→是双约当同态，当且仅当φ是一元、保持可逆性且联合连续的。另外，如果A是可交换的，则φ是双同态。

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Gleason–Kahane–Żelazko Theorem for Bilinear Maps

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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来源期刊

Annales Mathematicae Silesianae Mathematics-Mathematics (all)

CiteScore

0.60

自引率

25.00%

发文量

审稿时长

27 weeks