Duality Maps in Banach Spaces
In trying to develop analogue of the identity (1.1) in Banach spaces more general than Hilbert spaces, one has to find a suitable replacement for inner product, ⟨.,.⟩. In this chapter, we present the notion of duality mappings which will provide us with a pairing between elements of a normed space E and elements of its dual space E*, which we shall also denote by ⟨.,.⟩ and will serve as a suitable analogue of the inner product in Hilbert spaces.
KeywordsHilbert Space Banach Space Normed Space Real Hilbert Space Real Banach Space
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