### Abstract

Original language | Unknown |
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Title of host publication | n/a |

Pages | 111--121 |

Publication status | Published - 1 Jan 2009 |

Event | 6th international ISAAC congress - Duration: 1 Jan 2007 → … |

### Conference

Conference | 6th international ISAAC congress |
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Period | 1/01/07 → … |

### Keywords

### Cite this

*n/a*(pp. 111--121)

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*n/a.*pp. 111--121, 6th international ISAAC congress, 1/01/07.

**A $C^*$-algebra of functional operators with shifts having a nonempty set of periodic points.** / Fernandes, Cláudio António Raínha Aires.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A $C^*$-algebra of functional operators with shifts having a nonempty set of periodic points.

AU - Fernandes, Cláudio António Raínha Aires

PY - 2009/1/1

Y1 - 2009/1/1

N2 - Let $B(L^2(T))$ be the $C^{*}$-algebra of all bounded linear operators acting on $L^2(T)$, where $T$ is the unit circle in $C$, and let $G$ be an amenable discrete group of orientation-preserving homeomorphisms of $T$ onto itself such that all $gın G\setminus\{e\}$ have piecewise continuous derivatives $g'$ and the same nonempty set $\Lambda$ of periodic points, and there is a point $t ın\Lambda$ with the finite $G$-orbit. The authors study the invertibility in the $C^{*}$-subalgebra of $B(L^2(T))$ generated by all multiplication operators by piecewise slowly oscillating functions and by the group $U_G=\{U_g: g ın G, U_g(\Phi)(t)=|g'(t)|^{(1/2)} \Phi(g(t))\}$ of unitary operators.

AB - Let $B(L^2(T))$ be the $C^{*}$-algebra of all bounded linear operators acting on $L^2(T)$, where $T$ is the unit circle in $C$, and let $G$ be an amenable discrete group of orientation-preserving homeomorphisms of $T$ onto itself such that all $gın G\setminus\{e\}$ have piecewise continuous derivatives $g'$ and the same nonempty set $\Lambda$ of periodic points, and there is a point $t ın\Lambda$ with the finite $G$-orbit. The authors study the invertibility in the $C^{*}$-subalgebra of $B(L^2(T))$ generated by all multiplication operators by piecewise slowly oscillating functions and by the group $U_G=\{U_g: g ın G, U_g(\Phi)(t)=|g'(t)|^{(1/2)} \Phi(g(t))\}$ of unitary operators.

KW - functional operator

KW - invertibility

KW - representations of $C^$-algebras

KW - $C^$-algebra

KW - amenable group

M3 - Conference contribution

SN - 978-981-283-732-5/hbk

SP - 111

EP - 121

BT - n/a

ER -