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MATHEMATICS
Ultrapowers of Banach algebras
A. Ebadian, A.Jabbari Urmia University, 24, Beneshti (Daneshkade) st., Urmia, Iran
Abstract:
In this paper, we consider ultrapowers of Banach algebras as Banach algebras and the product $\bigcirc_{(J,\mathcal{U })}$ on the second dual of Banach algebras. For a Banach algebra $A$, we show that if there is a continuous derivation from $A$ into itself, then there is a continuous derivation from $(A^{**},\bigcirc_{(J,\mathcal{U})})$ into it. Moreover, we show that if there is a continuous derivation from $A$ into $X^{**}$, where $X$ is a Banach A-bimodule, then there is a continuous derivation from $A$ into ultrapower of $X$ i. e., $(X)_\mathcal{U}$ . Ultra (character) amenability of Banach algebras is investigated and it will be shown that if every continuous derivation from $A$ into $(X)_\mathcal{U}$ is inner, then $A$ is ultra amenable. Some results related to left (resp. right) multipliers on $(A^{**}, \bigcirc_{(J,\mathcal{U})})$ are also given.
Keywords:
amenability, arens products, derivation, multiplier, ultrapower, ultra amenable, ultra character amenability.
Received: 05.05.2022 Revised: 10.02.2022 Accepted: 03.03.2022
Citation:
A. Ebadian, A.Jabbari, “Ultrapowers of Banach algebras”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9:3 (2022), 527–541; Vestn. St. Petersbg. Univ., Math., 9:3 (2022), 527–541
Linking options:
https://www.mathnet.ru/eng/vspua32 https://www.mathnet.ru/eng/vspua/v9/i3/p527
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Abstract page: | 18 | Full-text PDF : | 8 | References: | 8 |
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