Abstract
We begin by recollecting the basic definitions and theorems:
There are many surprising aspects to the infinitely many directions in an infinite-dimensional space. For this reason it is necessary to investigate carefully which of the familiar properties of finite-dimensional spaces carry over unchanged and which do not.
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Thirring, W. (2002). The Mathematical Formulation of Quantum Mechanics. In: Quantum Mathematical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05008-8_2
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