 Lambda-injective normed space

For $\lambda \ge 1$, a normed vector space $X$ is lambda-injective when every bounded linear operator from a subspace $Y$ of any normed space $Z$ into $X$ extends to $Z$ with the displayed norm bound. The space of bounded scalar functions on an index set is 1-injective: extend each coordinate functional by the Hahn-Banach theorem and reassemble it using the coordinate functional representation of an operator into bounded indexed functions.