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Recurrence of Cosine Operator Functions on Groups

  Published:2016-03-18
 Printed: Dec 2016
  • Chung-Chuan Chen,
    Department of Mathematics Education, National Taichung University of Education, Taiwan
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Abstract

In this note, we study the recurrence and topologically multiple recurrence of a sequence of operators on Banach spaces. In particular, we give a sufficient and necessary condition for a cosine operator function, induced by a sequence of operators on the Lebesgue space of a locally compact group, to be topologically multiply recurrent.
Keywords: topologically multiple recurrence, recurrence, topological transitivity, hypercyclicity, cosine operator function topologically multiple recurrence, recurrence, topological transitivity, hypercyclicity, cosine operator function
MSC Classifications: 47A16, 54B20, 43A15 show english descriptions Cyclic vectors, hypercyclic and chaotic operators
Hyperspaces
$L^p$-spaces and other function spaces on groups, semigroups, etc.
47A16 - Cyclic vectors, hypercyclic and chaotic operators
54B20 - Hyperspaces
43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.
 

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