# Hypercyclicity of Semigroups is a Very Unstable Property

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 7, page 148-160
- ISSN: 0973-5348

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topDesch, W., and Schappacher, W.. "Hypercyclicity of Semigroups is a Very Unstable Property." Mathematical Modelling of Natural Phenomena 3.7 (2008): 148-160. <http://eudml.org/doc/222341>.

@article{Desch2008,

abstract = {
Hypercyclicity of C0-semigroups is a very unstable property: We give examples to
show that adding arbitrary small constants or a bounded rank one operator to the generator of a
hypercyclic semigroup can destroy hypercyclicity. Also the limit of hypercyclic semigroups (even
in operator norm topology) need not be hypercyclic, and a hypercyclic semigroup can be the limit
of nonhypercyclic ones. Hypercyclicity is not inherited by the Yosida approximations. Finally, the
restriction of a hypercyclic nonnegative semigroup in a Banach lattice to the positive cone may be
far from hypercyclic.
},

author = {Desch, W., Schappacher, W.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {hypercyclic semigroups; perturbation},

language = {eng},

month = {10},

number = {7},

pages = {148-160},

publisher = {EDP Sciences},

title = {Hypercyclicity of Semigroups is a Very Unstable Property},

url = {http://eudml.org/doc/222341},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Desch, W.

AU - Schappacher, W.

TI - Hypercyclicity of Semigroups is a Very Unstable Property

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/10//

PB - EDP Sciences

VL - 3

IS - 7

SP - 148

EP - 160

AB -
Hypercyclicity of C0-semigroups is a very unstable property: We give examples to
show that adding arbitrary small constants or a bounded rank one operator to the generator of a
hypercyclic semigroup can destroy hypercyclicity. Also the limit of hypercyclic semigroups (even
in operator norm topology) need not be hypercyclic, and a hypercyclic semigroup can be the limit
of nonhypercyclic ones. Hypercyclicity is not inherited by the Yosida approximations. Finally, the
restriction of a hypercyclic nonnegative semigroup in a Banach lattice to the positive cone may be
far from hypercyclic.

LA - eng

KW - hypercyclic semigroups; perturbation

UR - http://eudml.org/doc/222341

ER -

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