# On the norm-closure of the class of hypercyclic operators

Annales Polonici Mathematici (1997)

- Volume: 65, Issue: 2, page 157-161
- ISSN: 0066-2216

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topChristoph Schmoeger. "On the norm-closure of the class of hypercyclic operators." Annales Polonici Mathematici 65.2 (1997): 157-161. <http://eudml.org/doc/269977>.

@article{ChristophSchmoeger1997,

abstract = {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.},

author = {Christoph Schmoeger},

journal = {Annales Polonici Mathematici},

keywords = {hypercyclic operators; Weyl spectrum},

language = {eng},

number = {2},

pages = {157-161},

title = {On the norm-closure of the class of hypercyclic operators},

url = {http://eudml.org/doc/269977},

volume = {65},

year = {1997},

}

TY - JOUR

AU - Christoph Schmoeger

TI - On the norm-closure of the class of hypercyclic operators

JO - Annales Polonici Mathematici

PY - 1997

VL - 65

IS - 2

SP - 157

EP - 161

AB - 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.

LA - eng

KW - hypercyclic operators; Weyl spectrum

UR - http://eudml.org/doc/269977

ER -

## References

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- [8] C. Schmoeger, Ascent, descent and the Atkinson region in Banach algebras, II, Ricerche Mat. 42 (1993), 249-264. Zbl0807.46054

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