论文信息 - Approximately finite-dimensional Banach spaces

Approximately finite-dimensional Banach spaces

Abstract A Banach space is said to be approximately finite-dimensional if it has a nonstandard hull linearly isometric to a hyperfinite-dimensional Banach space or, equivalently, if an ultrapower is linearly isometric to an ultraproduct of finite-dimensional spaces. It is shown that the space C ( K ) of continuous functions on a compact Hausdorff space K is approximately finite-dimensional if and only if K is totally disconnected and contains a dense subset of isolated points.

L. C Moore | L. Moore

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