Taiwanese Journal of Mathematics

Approximate Cyclic Amenability of $T$-Lau Product of Banach Algebras

Hossein Javanshiri

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Abstract

Associated with two Banach algebras $\mathcal{A}$ and $\mathcal{B}$ and a norm decreasing homomorphism $T: \mathcal{B} \to \mathcal{A}$, there is a certain Banach algebra product $\mathcal{M}_T := \mathcal{A} \times_T \mathcal{B}$, which is a splitting extension of $\mathcal{B}$ by $\mathcal{A}$. In this paper, we investigate approximate cyclic amenability of $\mathcal{M}_T$ which has been introduced and studied by Esslamzadeh and Shojaee in [5]. In particular, apart from the characterization of all cyclic derivations on the Banach algebra $\mathcal{M}_T$, we improve the results of [1, 2] for cyclic amenability of $\mathcal{M}_T$. These results paves the way for obtaining new results for (approximate) cyclic amenability of the Banach algebra $\mathcal{A} \times \mathcal{B}$ equipped with the coordinatewise product algebra and $\ell^1$-norm.

Article information

Source
Taiwanese J. Math., Volume 20, Number 5 (2016), 1139-1147.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874521

Digital Object Identifier
doi:10.11650/tjm.20.2016.7154

Mathematical Reviews number (MathSciNet)
MR3555893

Zentralblatt MATH identifier
1357.46039

Subjects
Primary: 46H05: General theory of topological algebras 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Secondary: 46H99: None of the above, but in this section

Keywords
Banach algebra $T$-Lau product cyclic derivation approximate cyclic amenability

Citation

Javanshiri, Hossein. Approximate Cyclic Amenability of $T$-Lau Product of Banach Algebras. Taiwanese J. Math. 20 (2016), no. 5, 1139--1147. doi:10.11650/tjm.20.2016.7154. https://projecteuclid.org/euclid.twjm/1498874521


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References

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