E be a subset of a normed space X and Y = Span E and a € X. Show thatLeta € Ỹ if and only if f(a) = 0 whenever f € X' and f is zero everywhere on E.Y

To find: a∈Y¯, and f(a) = 0 whenever f∈Xι and f is 0 everywhere on E.

Answered: E be a subset of a normed space X and Y…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 4E: 4. Let , where is nonempty. Prove that a has left inverse if and only if for every subset of .

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E be a subset of a normed space X and Y = Span E and a € X. Show that Let a € Ỹ if and only if f(a) = 0 whenever f € X' and f is zero everywhere on E.