Cyclic vector

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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[edit]


  1. ^ Halmos, Paul R. (1982). "Cyclic Vectors". A Hilbert Space Problem Book. Graduate Texts in Mathematics. 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.