Norms in product spaces which preserve approximation properties
Copyright policy )Norms in product spaces which preserve approximation properties
SynopsisLet E1 and E2 be real normed linear spaces such that the dimension of any of them is at least 2. We prove that the norms in E1 × E2 which verify a simple property of monotonicity with regard to the initial norms in E1 and E2 are the only norms in E1 × E2 which preserve best linear approximations, in the sense that ifyk ∊ Lk is best approximation to xk from the linear subspace Lk, (k = 1,2), then (y1, y2) is best approximation to (x1, x2) from L1 × L2.
A-norm, Geometry and structure of normed linear spaces, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Isomorphic theory (including renorming) of Banach spaces, orthogonal in the Birkhoff sense, best approximations, M-norm
A-norm, Geometry and structure of normed linear spaces, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Isomorphic theory (including renorming) of Banach spaces, orthogonal in the Birkhoff sense, best approximations, M-norm
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