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Article
Notes on hypercyclic operators
Acta Sci. Math. (Szeged) (1993)
  • Valentin Matache, University of Nebraska at Omaha
Abstract
The author considers operators T acting on complex separable Banach spaces. The set {x, T x, T2x, . . . , T nx, . . .} is called the orbit of x under T. If dense orbits exist T is called hypercyclic. If the spectrum of a hypercyclic operator can be represented as the union of two nonvoid, compact, mutually disjoint sets then each of these sets must have nonvoid intersection with the unit circle. No nonzero reducing subspace of a hypercyclic operator T reduces T to a normal, respectively to a compact operator. For Hilbert space contractions A if λA is hypercyclic for some complex λ then A is in C0. \ C0 .
Keywords
  • 47A15,
  • 47A20
Disciplines
Publication Date
1993
Publisher Statement
Copyright © 1993 ACTA.
Citation Information
Valentin Matache. "Notes on hypercyclic operators" Acta Sci. Math. (Szeged) Vol. 58 Iss. 1-4 (1993) p. 401 - 410
Available at: http://works.bepress.com/valentin-matache/33/