Cyclic vector

In the mathematics of operator theory, an operator $A$ on an (infinite-dimensional) Banach space or Hilbert space $H$ has a cyclic vector $f$ if the vectors $f, A f, A^{2} f, \dots$ span $H$ . Equivalently, $f$ is a cyclic vector for $A$ in case the set of all vectors of the form $p (A) f$ , where $p$ varies over all polynomials, is dense in $H$ .

See also

Cyclic and separating vector

References

↑ Halmos (1982).
↑ "Cyclic vector". Encyclopedia of Mathematics.

Halmos, Paul R. (1982). "Cyclic vectors". A Hilbert Space Problem Book. Graduate Texts in Mathematics. Vol. 19. New York: Springer. pp. 86–89. doi:10.1007/978-1-4684-9330-6_18. ISBN 978-1-4684-9332-0.

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