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.
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© 2009 Springer-Verlag Berlin Heidelberg
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(2009). Duality Maps in Banach Spaces. In: Geometric Properties of Banach Spaces and Nonlinear Iterations. Lecture Notes in Mathematics, vol 1965. Springer, London. https://doi.org/10.1007/978-1-84882-190-3_3
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DOI: https://doi.org/10.1007/978-1-84882-190-3_3
Publisher Name: Springer, London
Print ISBN: 978-1-84882-189-7
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