Cyclic Vector

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

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

is dense in . In this case, the operator 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

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References

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

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Cite this as:

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

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