Bulletin of the
Korean Mathematical Society BKMS

For a metric space $(X,d)$ and $ \alpha>0. $ We study the structure and properties of vector-valued Lipschitz algebra $Lip_{\alpha}(X,E)$ and $lip_{\alpha}(X,E)$ of order $ \alpha. $ We investigate the approximate and Character amenability of vector-valued Lipschitz algebras.

Keywords: approximately amenability, character amenability, Lipschitz algebra, metric space, vector-valued functions

MSC numbers: Primary 46B28, 46M05, 46J10