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Tag Archives: subspace
Subspaces and projections
Let be a closed subspace of a Banach space . In general, there is no linear projection , the canonical example being in . At least we can construct a projection when is finite-dimensional. The one-dimensional case is easy: take … Continue reading
Nearest point projection, part II: beware of two-dimensional gifts
To avoid the complications from the preceding post, let’s assume that is a uniformly convex Banach space: such a space is automatically reflexive, and therefore any closed subspace has a well-defined nearest point projection . Recalling that in a Hilbert … Continue reading
Nearest point projection, part I: eschewing transliterations
A subset of a metric space is called a Чебышёв (Chebyshev) set if for every there exists such that for all . In words, for each point of the space there is a well-defined nearest point of . We can … Continue reading
