Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 469-493.

Approximation of chaotic operators

Authors: Bingzhe Hou (1), Geng Tian (2), and Sen Zhu (3)
Author institution: (1) Dept. of Mathematics, Jilin University, Changchun, 130012, P.R. China
(2) Dept. of Mathematics, Jilin University, Changchun, 130012, P.R. China
(3) Dept. of Mathematics, Jilin University, Changchun, 130012, P.R. China

Summary: As it is well-known, the concept "hypercyclicity" in operator theory is the same as the concept "transitivity" in dynamical system. Now the class of hypercyclic operators is well studied. Following the idea of research in hypercyclic operators, we consider the classes of operators with other kinds of chaotic properties in this article. First, the closures and the interiors of the set of all Li-Yorke chaotic operators or all distributionally chaotic operators are discussed. Then we will show the connectedness of these sets.

Keywords: spectrum, Fredholm index, Li-Yorke chaotic operator, distributionally chaotic operator, hypercyclic operator, closure, interior, connectedness

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