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Keywords:
approximate biflatness; Johnson pseudo-contractibility; Lipschitz algebra; triangular Banach algebra
approximate biflatness; Johnson pseudo-contractibility; Lipschitz algebra; triangular Banach algebra
Summary:
We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space $X$, the Lipschitz algebras ${\rm Lip}_{\alpha}(X)$ and ${\rm lip}_{\alpha}(X)$ are approximately biflat if and only if $X$ is finite, provided that $0<\alpha<1$. We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.
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