Projection constants and spaces of continuous functions

摘要: 1. Theorems. A real Banach space X will be called injective(2) if for every Y and subspace YO, linear operation(') To : YO -* can extended to a operation T Y-* X. An equivalent condition is this: Z containing as subspace, there exists projection from onto The class of injective spaces usually denoted by $3, $,, denotes the all which such always found with norm _ s. If E then 1S some s ? 1; infimum p(X) numbers constant X, exact attained. Any isometrically embedded into belonging $31; YE 3, only projection(4) P Z-Y || |j < this particular space, best being independent choice embedding(5). 0 we shall write p(X)M = o 31 nicely characterized(6): e 1 isometric C(S) S extremally disconnected compact. known examples $ are isomorphic these $1(7).