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Weak convergence (Hilbert space)
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Weak convergence (Hilbert space) : ウィキペディア英語版
Weak convergence (Hilbert space)

In mathematics, weak convergence in a Hilbert space is convergence of a sequence of points in the weak topology.
==Definition==
A sequence of points (x_n) in a Hilbert space ''H'' is said to converge weakly to a point ''x'' in ''H'' if
:\langle x_n,y \rangle \to \langle x,y \rangle
for all ''y'' in ''H''. Here, \langle \cdot, \cdot \rangle is understood to be the inner product on the Hilbert space. The notation
:x_n \rightharpoonup x
is sometimes used to denote this kind of convergence.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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