Cyclic vector

An operator A on an (infinite dimensional) Banach space or Hilbert space H has a cyclic vector f if the vectors f, Af, A2f,... 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.[1][2]

References

  1. ↑ A Hilbert Space Problem Book. pp. 86–89.
  2. ↑ "Cyclic vector". Encyclopedia of Mathematics.


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