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LIMITS OF HYPERCYCLIC AND SUPERCYCLIC OPERATOR MATRICES

Part of: General theory of linear operators

Published online by Cambridge University Press:  01 December 2008

XIAOHONG CAO
XIAOHONG CAO*
Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, People’s Republic of China (email: xiaohongcao@snnu.edu.cn)
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Abstract

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An operator A on a complex, separable, infinite-dimensional Hilbert space H is hypercyclic if there is a vector x∈H such that the orbit {x,Ax,A2x,…} is dense in H. Using the character of the analytic core and quasinilpotent part of an operator A, we explore the hypercyclicity for upper triangular operator matrix

Keywords

hyperbolicityanalytic corequasi-nilpotent partspectrum

MSC classification

Secondary: 47A53: (Semi-) Fredholm operators; index theories 47A55: Perturbation theory 47A15: Invariant subspaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 3 , December 2008 , pp. 367 - 376
Copyright
Copyright © Australian Mathematical Society 2009

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