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Prove that if X is a Banach space, X ∕= {0}, then there is a non-zero biounded linear functional on X.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...

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Prove that if X is a Banach space, X ∕= {0}, then there is a
non-zero biounded linear functional on X.

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