Abstract
The dual of X* is another Banach space X**. This is called the second dual or the bidual of X. Let J be the map from X into X** that associates with x ∈ X the element F x ∈ X** defined as
Then J is a linear map and ‖Jx‖ = ‖x‖. (See (9.2).) Thus J is an isometric imbedding and we can regard X as a subspace of X**.
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© 2009 Hindustan Book Agency
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Bhatia, R. (2009). The Second Dual and the Weak* Topology. In: Notes on Functional Analysis. Texts and Readings in Mathematics, vol 50. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-45-3_10
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DOI: https://doi.org/10.1007/978-93-86279-45-3_10
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-89-0
Online ISBN: 978-93-86279-45-3
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