On the norm-closure of the class of hypercyclic operators

• Autorzy: Christoph Schmoeger
• Języki publikacji: EN

Abstrakty

EN

Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if $f(σ_{W}(T)) ∪ {z ∈ ℂ: |z| = 1}$ is connected, where $σ_{W}(T)$ denotes the Weyl spectrum of T.

Słowa kluczowe

EN

hypercyclic operators

Kategorie tematyczne

• 47B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996-1997
• Tom: 65
• Numer: 2
• Strony: 157-161

Daty

wydano

1997

otrzymano

1995-08-21

poprawiono

1996-04-10

Twórcy

autor

Christoph Schmoeger

• Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany

Bibliografia

• [1] C. Bosch, C. Hernández, E. De Oteyza and C. Pearcy, Spectral pictures of functions of operators, J. Operator Theory 8 (1982), 391-400.
• [2] B. Gramsch and D. Lay, Spectral mapping theorems for essential spectra, Math. Ann. 192 (1971), 17-32.
• [3] D. A. Herrero, Limits of hypercyclic and supercyclic operators, J. Funct. Anal. 99 (1991), 179-190.
• [4] G. Herzog and C. Schmoeger, On operators T such that f(T) is hypercyclic, Studia Math. 108 (1994), 209-216.
• [5] H. Heuser, Funktionalanalysis, 2nd ed., Teubner, Stuttgart, 1986.
• [6] K. K. Oberai, Spectral mapping theorem for essential spectra, Rev. Roumaine Math. Pures Appl. 25 (1980), 365-373.
• [7] C. Pearcy, Some Recent Developments in Operator Theory, CBMS Regional Conf. Ser. in Math. 36, Amer. Math. Soc., Providence, 1978.
• [8] C. Schmoeger, Ascent, descent and the Atkinson region in Banach algebras, II, Ricerche Mat. 42 (1993), 249-264.