Epsilon-hypercyclic operators

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00374204" target="_blank" >RIV/67985840:_____/10:00374204 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0143385709000765" target="_blank" >http://dx.doi.org/10.1017/S0143385709000765</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0143385709000765" target="_blank" >10.1017/S0143385709000765</a>

Result language
angličtina
Original language name
Epsilon-hypercyclic operators
Original language description
Let X be a separable infinite-dimensional Banach space, and T a bounded linear operator on X; T is hypercyclic if there is a vector x in X with dense orbit under the action of T. For a fixed epsilon is an element of (0, 1), we say that T is epsilon-hypercyclic if there exists a vector x in X such that for every non-zero vector y is an element of X there exists an integer n with parallel to T(n)x - y parallel to <= epsilon parallel to y parallel to. The main result of this paper is a construction of a bounded linear operator T on the Banach space l(1) which is epsilon-hypercyclic without being hypercyclic. This answers a question from V. Muller [Three problems, Mini-Workshop: Hypercyclicity and linear chaos, organized by T. Bermudez, G. Godefroy, K.-G.Grosse-Erdmann and A. Peris. Oberwolfach Rep. 3 (2006), 2227-2276].
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA201%2F06%2F0128" target="_blank" >GA201/06/0128: Methods of function theory and Banach algebras in operator theory III.</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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