A separating vector is defined for a subalgebra 
of the algebra 
of bounded linear transformations from a Hilbert
space 
into itself. A vector 
is a separating vector for 
if the only operator 
satisfying 
is the zero operator 
.
Separating Vector
See also
Cyclic Vector, Functional Analysis, Hilbert Space, Reeh-Schlieder Theorem, Separable SpacePortions of this entry contributed by Christopher Stover
Explore with Wolfram|Alpha
References
Conway, J. B. A Course in Functional Analysis, 2nd ed. New York: Springer-Verlag, 1997.Referenced on Wolfram|Alpha
Separating VectorCite this as:
Weisstein, Eric W., with contributions by Christopher Stover. "Separating Vector." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SeparatingVector.html