Abstract
In a Hilbert space, we can introduce the notion of orthogonal coordinates through an orthogonal base, and these coordinates are the values of bounded linear functional defined by the vectors of the base. This suggests that we consider continuous linear functional, in a linear topological space, as generalized coordinates of the space. To ensure the existence of non-trivial continuous linear functional in a general locally convex linear topological space, we must rely upon the Hahn-Banach extension theorems.
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© 1995 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1995). The Hahn-Banach Theorems. In: Functional Analysis. Classics in Mathematics, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61859-8_5
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DOI: https://doi.org/10.1007/978-3-642-61859-8_5
Publisher Name: Springer, Berlin, Heidelberg
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