This article provides insufficient context for those unfamiliar with the subject. Please help improve the article by providing more context for the reader. (October 2018) (Learn how and when to remove this template message)

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]

See also

References

  1. ^ Halmos, Paul R. (1982). "Cyclic Vectors". A Hilbert Space Problem Book. Graduate Texts in Mathematics. Vol. 19. pp. 86–89. doi:10.1007/978-1-4684-9330-6_18. ISBN 978-1-4684-9332-0.
  2. ^ "Cyclic vector". Encyclopedia of Mathematics.


Categories