Respected readers, authors and reviewers, you can add comments to this page on any questions about the contribution, review, editing and publication of this journal. We will give you an answer as soon as possible. Thank you for your support!
LIU Yang, CAO Xiao-hong. Hypercyclicity and topological uniform descent of bounded linear operators[J]. Journal of East China Normal University (Natural Sciences), 2013, (5): 130-135, 143.
Citation:
LIU Yang, CAO Xiao-hong. Hypercyclicity and topological uniform descent of bounded linear operators[J]. Journal of East China Normal University (Natural Sciences), 2013, (5): 130-135, 143.
LIU Yang, CAO Xiao-hong. Hypercyclicity and topological uniform descent of bounded linear operators[J]. Journal of East China Normal University (Natural Sciences), 2013, (5): 130-135, 143.
Citation:
LIU Yang, CAO Xiao-hong. Hypercyclicity and topological uniform descent of bounded linear operators[J]. Journal of East China Normal University (Natural Sciences), 2013, (5): 130-135, 143.
By using the property of topological uniform descent, this
paper gave the judgement for an operator $A\in\overline{HC(H)}$,
where $\overline{HC(H)}$ denoting the norm-closure of the class of
all the hypercyclic operators on an infinite dimensional separable
complex Hilbert space $H$.
{1}GRABINER S. Uniform ascent and descent of bounded operators[J]. JMath Soc Japan, 1982, 34(2): 317-337.{2}AIENA P. Fredholm and Local Spectral Theory, with Applications toMultipliers[M]. Dordrecht: Kluwer Academic Publishers, 2004.{3}LAURSEN K B, NEUMANN M M. An Introduction to Local SpectralTheorey[M]. London Math Soc Monogr New Ser 20. New York: ClarendonPress, 2000.{4}FINCH J K. The single valued extension property on a Banachspace[J]. Pacific J Math, 1975, 58(1): 61-69.{5}HERRERO D A. Limits of hypercyclic and supercyclic operators[J].Journal of Functional Analysis, 1991, 99: 179-190.{6}ZHU S, LI CH G. SVEP and compact perturbation[J]. Journal ofMathematical Analysis and Applications, 2011, 380: 69-75.{7}JIANG Q F, ZHONG H J, ZENG Q P. Topological uniform descent andlocalized SVEP[J]. Journal of Mathematical Analysis andApplications, 2012, 390: 355-361.