Abstract
In this chapter we shall prove that א0-dimensional sesquilinear spaces are orthogonal sums of lines and planes and we characterize the cases where a decomposition into mutually orthogonal lines is impossible. The problem of “normalizing” bases brings us to stability and the beginner is confronted with the first Ping-Pong style proof with its characteristic back-and-forth argument (Theorem 2). These matters are basic and their knowledge is tacitly assumed in the rest of the book.
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References to Chapter II
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Gross, H. (1979). Diagonalization of א0-Forms. In: Quadratic Forms in Infinite Dimensional Vector Spaces. Progress in Mathematics, vol 1. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3542-7_3
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DOI: https://doi.org/10.1007/978-1-4899-3542-7_3
Publisher Name: Birkhäuser, Boston, MA
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