Given a subalgebra 
of the algebra 
of bounded linear
transformations from a Hilbert space 
onto itself, the vector 
is a separating vector for 
if the only operator 
satisfying 
is the zero operator 
.
Separating Vector
See also
Functional Analysis, Hilbert Space, Separable SpaceThis entry contributed by Christopher Stover
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References
Conway, J. B. A Course in Functional Analysis, 2nd ed. New York: Springer-Verlag, 1997.Cite this as:
Stover, Christopher. "Separating Vector." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SeparatingVector.html