Cyclic Operator

A cyclic operator is a bounded linear operator on a Hilbert space for which there exists a vector such that the linear span of the orbit

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

is dense in . In this case, the vector is said to be a cyclic vector.

See also

Bounded Operator, Cyclic Vector, 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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Cyclic Operator

Cite this as:

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

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