Answer to Question #272130 in Functional Analysis for Prathibha Rose

Functional Analysis

Question #272130

Let X be a normed linear space and Y a closed subspace of X

with Y ≠ X ,if 0 < 𝑟 < 1 prove that there exist

𝑋𝑟 𝜖 𝑋 𝑠𝑢ch that ||Xr|| = 1And 𝑟 < 𝑑 𝑋𝑟

, 𝑌 ≤ 1

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