TOPICS
Search

Cyclic Vector


A vector v on a Hilbert space H is said to be cyclic if there exists some bounded linear operator T on H so that the set of orbits

 {T^iv}_(i=0)^infty={v,Tv,T^2v,...}

is dense in H. In this case, the operator T is said to be a cyclic operator.


See also

Bounded Operator, Cyclic Operator, Hilbert Space, Linear Operator, Map Orbit

This entry contributed by Christopher Stover

Explore with Wolfram|Alpha

References

Wu, P. Y. "Sums and Products of Cyclic Operators." Proc. Amer. Math. Soc. 122, 1053-1063, 1994.

Cite this as:

Stover, Christopher. "Cyclic Vector." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CyclicVector.html

Subject classifications