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
- Ladder
- Ladder Graph
- Lagrange Bracket
- Lagrange-Bürmann Theorem
- Lagrange Expansion
- Lagrange Interpolating Polynomial
- Lagrange Inversion Theorem
- Lagrange Multiplier
- Lagrange Number (Diophantine Equation)
- Lagrange Number (Rational Approximation)
- Lagrange Polynomial
- Lagrange Remainder
- Lagrange Resolvent
- Lagrange's Continued Fraction Theorem
- Lagrange's Equation
- Lagrange's Four-Square Theorem
- Lagrange's Group Theorem
- Lagrange's Identity
- Lagrange's Interpolating Fundamental Polynomial
- Lagrange's Lemma
- Lagrange Spectrum
- Lagrangian Coefficient
- Lagrangian Derivative
- Laguerre Differential Equation
- Laguerre-Gauss Quadrature