An operator extension of a linear operator 
is a linear
operator 
on the same Hilbert space 
such that 
and 
for every vector 
. Here, 
and 
are the respective domains;
is said to extend 
.
Operator Extension
See also
Extension Problem, Hilbert Space, Linear OperatorThis entry contributed by Christopher Stover
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References
Loss, M. "About Closed Operators." 2013. https://loss.math.gatech.edu/13Springtea/closedoperators.pdf.Referenced on Wolfram|Alpha
Operator ExtensionCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Operator Extension." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/OperatorExtension.html