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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.
Original languageUnknown
Title of host publicationn/a
Pages111--121
Publication statusPublished - 1 Jan 2009
Event6th international ISAAC congress -
Duration: 1 Jan 2007 → …

Conference

Conference6th international ISAAC congress
Period1/01/07 → …

Keywords

    Cite this

    @inproceedings{9057740d63464942885d0a637fb00e6c,
    title = "A $C^*$-algebra of functional operators with shifts having a nonempty set of periodic points.",
    abstract = "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.",
    keywords = "functional operator, invertibility, representations of $C^*$-algebras, $C^*$-algebra, amenable group",
    author = "Fernandes, {Cl{\'a}udio Ant{\'o}nio Ra{\'i}nha Aires}",
    year = "2009",
    month = "1",
    day = "1",
    language = "Unknown",
    isbn = "978-981-283-732-5/hbk",
    pages = "111----121",
    booktitle = "n/a",

    }

    Fernandes, CARA 2009, A $C^*$-algebra of functional operators with shifts having a nonempty set of periodic points. in 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.

    n/a. 2009. p. 111--121.

    Research output: Chapter in Book/Report/Conference proceedingConference 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 -