# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1910.43341

Hilbert Space Operators in Quantum Physics, 1-40, 2008
The notion of a vector space is obtained by axiomatization of the properties of the threedimensional space of Euclidean geometry, or of configuration spaces of classical mechanics. A vector (or linear) space V is a set {x, y,...} equipped with the operations of summation,[x, y] x+ y V, and multiplication by a complex or real number ,[, x] x V, such that (i) The summation is commutative, x+ y= y+ x, and associative,(x+ y)+ z= x+(y+ z). There exist a zero element 0 V, and an inverse element x V, to any x V so that x+ 0= x and x+( x)= 0 holds for all x V.(ii) (x)=() x and 1x= x.(iii) The summation and multiplication are distributive, (x+ y)= x+ y and (+ ) x= x+ x.
```@inproceedings{ji2008some,
title={Some notions from functional analysis},
author={Ji Blank, Pavel Exner, and Miloslav Havlek},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020141626019652870},
booktitle={Hilbert Space Operators in Quantum Physics},
pages={1-40},
year={2008},
}
```
Ji Blank, Pavel Exner, and Miloslav Havlek. Some notions from functional analysis. 2008. In Hilbert Space Operators in Quantum Physics. pp.1-40. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020141626019652870.