Strong convergence, also called norm convergence, of a sequence 
to a vector 
in a normed
space means that, as 
,
 |
In an inner product space, strong convergence implies weak convergence, but the converse does not hold in general.
Strong Convergence
See also
Convergence, Convergent Sequence, Inner Product Space, Normed Space, Weak ConvergenceExplore with Wolfram|Alpha
References
Kreyszig, E. Introductory Functional Analysis with Applications. New York: Wiley, 1989.Referenced on Wolfram|Alpha
Strong ConvergenceCite this as:
Weisstein, Eric W. "Strong Convergence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StrongConvergence.html