Duality Maps in Banach Spaces

Part of the Lecture Notes in Mathematics book series (LNM, volume 1965)

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.


Hilbert Space Banach Space Normed Space Real Hilbert Space Real Banach Space 
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© Springer-Verlag Berlin Heidelberg 2009

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