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Search: All articles in the CMB digital archive with keyword bounded approximate identity

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1. CMB 2011 (vol 54 pp. 654)

Forrest, Brian E.; Runde, Volker
 Norm One Idempotent \$cb\$-Multipliers with Applications to the Fourier Algebra in the \$cb\$-Multiplier Norm For a locally compact group \$G\$, let \$A(G)\$ be its Fourier algebra, let \$M_{cb}A(G)\$ denote the completely bounded multipliers of \$A(G)\$, and let \$A_{\mathit{Mcb}}(G)\$ stand for the closure of \$A(G)\$ in \$M_{cb}A(G)\$. We characterize the norm one idempotents in \$M_{cb}A(G)\$: the indicator function of a set \$E \subset G\$ is a norm one idempotent in \$M_{cb}A(G)\$ if and only if \$E\$ is a coset of an open subgroup of \$G\$. As applications, we describe the closed ideals of \$A_{\mathit{Mcb}}(G)\$ with an approximate identity bounded by \$1\$, and we characterize those \$G\$ for which \$A_{\mathit{Mcb}}(G)\$ is \$1\$-amenable in the sense of B. E. Johnson. (We can even slightly relax the norm bounds.) Keywords:amenability, bounded approximate identity, \$cb\$-multiplier norm, Fourier algebra, norm one idempotentCategories:43A22, 20E05, 43A30, 46J10, 46J40, 46L07, 47L25

2. CMB 2001 (vol 44 pp. 504)

Zhang, Yong
 Weak Amenability of a Class of Banach Algebras We show that, if a Banach algebra \$\A\$ is a left ideal in its second dual algebra and has a left bounded approximate identity, then the weak amenability of \$\A\$ implies the (\$2m+1\$)-weak amenability of \$\A\$ for all \$m\geq 1\$. Keywords:\$n\$-weak amenability, left ideals, left bounded approximate identityCategories:46H20, 46H10, 46H25