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Let $A$ and $B$ be two Banach algebras and $T:B\to A$ be a bounded homomorphism, with $\|T\|\leq 1$. Recently, Dabhi, Jabbari and Haghnejad Azar (\textit{Acta Math. Sin. $($Engl. Ser.$)$} \textbf{31} (2015), no. 9, 1461--1474) obtained some results about the $n$-weak amenability of $A\times_T B$. In the present paper, we address a gap in the proof of these results and extend and improve them by discussing general necessary and sufficient conditions for $A\times_T B$ to be $n$-weakly amenable, for an integer $n\geq0$.
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참고문헌 (10)
참고문헌 신청
A. R. Khoddami / 2013 / n-weak amenability of T-Lau product of Banach algebras / Chamchuri J. Math 5 : 57 ~ 65
A. T.-M. Lau / 1983 / Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups / Fund. Math 118 (3) : 161 ~ 175
B. E. Johnson / 1988 / Derivations from L1(G) into L1(G) and L1(G), Harmonic analysis (Luxembourg, 1987) / Lecture Notes in Math. 1359 : 191 ~ 198
G. W. Bade / 1987 / Amenability and weak amenability for Beurling and Lipschitz algebras / Proc. London Math. Soc 55 (2) : 359 ~ 377
H. G. Dales / 1998 / Derivations into iterated duals of Banach algebras / Studia Math 128 (1) : 19 ~ 54
A. T.-M. Lau / 1983 / Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups / Fund. Math 118 (3) : 161 ~ 175
B. E. Johnson / 1988 / Derivations from L1(G) into L1(G) and L1(G), Harmonic analysis (Luxembourg, 1987) / Lecture Notes in Math. 1359 : 191 ~ 198
G. W. Bade / 1987 / Amenability and weak amenability for Beurling and Lipschitz algebras / Proc. London Math. Soc 55 (2) : 359 ~ 377
H. G. Dales / 1998 / Derivations into iterated duals of Banach algebras / Studia Math 128 (1) : 19 ~ 54
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