Weak Convergence
Weak convergence is usually either denoted 
or 
. A Sequence 
ofVectors in an Inner Product Space 
is called weakly convergent to a Vector in if
Every Strongly Convergent sequence is also weakly convergent (but the opposite does notusually hold). This can be seen as follows. Consider the sequence
that converges strongly to 
, i.e.,
as 
. Schwarz's Inequality now gives
The definition of weak convergence is therefore satisfied.See also Inner Product Space, Schwarz's Inequality, Strong Convergence
- H-Fractal
- H-Function
- Hh Function
- Higher Arithmetic
- Highest Weight Theorem
- HighLife
- Highly Abundant Number
- Highly Composite Number
- Higman-Sims Group
- Hilbert Basis Theorem
- Hilbert Curve
- Hilbert Function
- Hilbert Hotel
- Hilbert Matrix
- Hilbert Number
- Hilbert Polynomial
- Hilbert's Axioms
- Hilbert-Schmidt Norm
- Hilbert-Schmidt Theory
- Hilbert's Constants
- Hilbert's Inequality
- Hilbert's Nullstellansatz
- Hilbert Space
- Hilbert's Problems
- Hilbert's Theorem