Abstract
An operator A on a Hilbert space H has a cyclic vector f if the vectors f, Af, A 2 f,... 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. The simple unilateral shift has many cyclic vectors; a trivial example is e 0.
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© 1982 Springer-Verlag New York Inc
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Halmos, P.R. (1982). Cyclic Vectors. In: A Hilbert Space Problem Book. Graduate Texts in Mathematics, vol 19. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9330-6_18
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DOI: https://doi.org/10.1007/978-1-4684-9330-6_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9332-0
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