科研之友
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摘要
Let X, Y be real Banach spaces and epsilon > 0. A standard epsilon-isometry f : X -> Y is said to be (alpha, gamma)-stable (with respect to T : L(f) equivalent to (span) over bar f(X) -> X for some alpha, gamma, > 0) if T is a linear operator with parallel to T parallel to <= alpha such that Tf - Id is uniformly bounded by gamma epsilon. on X. The pair (X, Y) is said to be stable if every standard epsilon-isometry f : X -> Y is (alpha, gamma)-stable for some alpha, gamma > 0. The space X [Y] is said to be universally left [right]-stable if (X, Y) is always stable for every Y [X]. In this paper, we show that universally right-stable spaces are just Hilbert spaces; every injective space is universally left-stable; a Banach space X isomorphic to a subspace of l(infinity), is universally left-stable if and only if it is isomorphic to l(infinity); and a separable space X has the property that (X, Y) is left-stable for every separable Y if and only if X is isomorphic to c(0).
