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- W1998609898 abstract "1. Theorems. A real Banach space X will be called injective(2) if for every Banach space Y and subspace YO, every linear operation(') To : YO -* X can be extended to a linear operation T : Y-* X. An equivalent condition is this: for every Banach space Z containing X as a subspace, there exists a projection from Z onto X. The class of injective spaces is usually denoted by $3, and $,, denotes the class of all spaces X for which such a projection can always be found with norm _ s. If X E $3, then X E 1S for some s ? 1; the infimum p(X) of such numbers s is called the projection constant of X, and is called exact if the infimum is attained. Any Banach space Y can be isometrically embedded into a space Z belonging to $31; and YE 3, if and only if there exists a projection(4) P : Z-Y with || P |j < s from this particular space, the best constant being independent of the choice of Z and of the embedding(5). If X 0 3, we shall write p(X)M = o The class 31 is nicely characterized(6): X e 1 if and only if X is isometric to a space C(S) with S extremally disconnected and compact. The only known examples of spaces of $ are spaces isomorphic to these spaces of $1(7)." @default.
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- W1998609898 date "1963-01-01" @default.
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- W1998609898 title "Projection constants and spaces of continuous functions" @default.
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