It is certainly true that the concepts of algebraic bases and orthonormal bases are crucial to the study of finite dimensional vector spaces and Hilbert spaces, respectively. That is why one tries to find a corresponding concept in the study of Banach spaces. Although, using Zorn’s lemma, one can always establish the existence of an algebraic basis of a given Banach space, this isn’t really sufficient because such a basis does not provide information about the topology of the space.
KeywordsBanach Space Basic Sequence Separable Banach Space Unconditional Basis Basis Constant
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