Semigroup Forum

, Volume 92, Issue 3, pp 587–597 | Cite as

A note on the periodic decomposition problem for semigroups

  • Bálint FarkasEmail author


Given \(T_1,\dots , T_n\) commuting power-bounded operators on a Banach space we study under which conditions the equality \(\ker (T_1-\mathrm {I})\cdots (T_n-\mathrm {I})=\ker (T_1-\mathrm {I})+\cdots +\ker (T_n-\mathrm {I})\) holds true. This problem, known as the periodic decomposition problem, goes back to I. Z. Ruzsa. In this short note we consider the case when \(T_j=T(t_j), t_j>0, j=1,\dots , n\) for some one-parameter semigroup \((T(t))_{t\ge 0}\). We also look at a generalization of the periodic decomposition problem when instead of the cyclic semigroups \(\{T_j^n:n \in \mathbb {N}\}\) more general semigroups of bounded linear operators are considered.


Periodic decomposition problem \(C_0\)-(semi)group  Norm-continuous one-parameter semigroup Amenable semigroup 



The author was supported by the Hungarian Research Fund (OTKA-100461).


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and Natural SciencesUniversity of WuppertalWuppertalGermany

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