Deviation of elements of a Banach space from a system of subspaces
We prove that if X is a real Banach space, Y 1 ⊂ Y 2 ⊂ ... is a sequence of strictly embedded closed linear subspaces of X, and d 1 ≥ d 2 ≥ ... is a nonincreasing sequence converging to zero, then there exists an element x ∈ X such that the distance ρ(x, Y n ) from x to Y n satisfies the inequalities d n ≤ ρ(x, Y n ) ≤ 8d n for n = 1, 2, ....
KeywordsHilbert Space Banach Space Positive Integer STEKLOV Institute Number Sequence
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