Abstract
In this chapter, we continue our study of Banach and Hilbert spaces. Here, we mainly consider linear functionals, i.e., additive, homogeneous, and continuous number functions given on such spaces. The problems under consideration are mostly grouped around two fundamental facts, namely, the Hahn-Banach theorem on extensions of linear functionals and the Banach-Steinhaus theorem (the principle of uniform boundedness). The general form of linear continuous functionals in many important spaces and some geometric problems in the theory of Hilbert spaces are also investigated.
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© 1996 Birkhäuser Verlag
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Berezansky, Y.M., Sheftel, Z.G., Us, G.F. (1996). Linear Continuous Functionals and Dual Spaces. In: Functional Analysis. Operator Theory Advances and Applications, vol 85. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9185-1_7
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DOI: https://doi.org/10.1007/978-3-0348-9185-1_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9939-0
Online ISBN: 978-3-0348-9185-1
eBook Packages: Springer Book Archive