Jacobson Radical

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Agata Smoktunowicz - One of the best experts on this subject based on the ideXlab platform.

Antonios Manoussos - One of the best experts on this subject based on the ideXlab platform.

  • the Jacobson Radical for analytic crossed products
    Journal of Functional Analysis, 2001
    Co-Authors: Allan P Donsig, A Katavolos, Antonios Manoussos
    Abstract:

    We characterise the Jacobson Radical of an analytic crossed product C0(X)×φ Z+, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson Radical of analytic crossed products C0(X)×φ Zd+. This consists of all elements whose “Fourier coefficients” vanish on the recurrent points of the dynamical system (and the first one is zero). The multidimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.

  • the Jacobson Radical for analytic crossed products
    arXiv: Operator Algebras, 2000
    Co-Authors: Allan P Donsig, A Katavolos, Antonios Manoussos
    Abstract:

    We characterise the (Jacobson) Radical of the analytic crossed product of C_0(X) by the non-negative integers (Z_+), answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Radical of analytic crossed products of C_0(X) by (Z_+)^d. The Radical consists of all elements whose `Fourier coefficients' vanish on the recurrent points of the dynamical system (and the first one is zero). The multi-dimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.

Justin R Peters - One of the best experts on this subject based on the ideXlab platform.

  • semicrossed products of the disk algebra and the Jacobson Radical
    Canadian Mathematical Bulletin, 2014
    Co-Authors: Anchalee Khemphet, Justin R Peters
    Abstract:

    We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson Radical of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with zero hyperbolic step, the Jacobson Radical is nonzero and a proper subset of the set of quasinilpotent elements.

Anchalee Khemphet - One of the best experts on this subject based on the ideXlab platform.

  • semicrossed products of the disk algebra and the Jacobson Radical
    Canadian Mathematical Bulletin, 2014
    Co-Authors: Anchalee Khemphet, Justin R Peters
    Abstract:

    We consider semicrossed products of the disk algebra with respect to endomorphisms defined by finite Blaschke products. We characterize the Jacobson Radical of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic, we show that the semicrossed product contains no nonzero quasinilpotent elements. However, if the finite Blaschke product is hyperbolic or parabolic with zero hyperbolic step, the Jacobson Radical is nonzero and a proper subset of the set of quasinilpotent elements.

  • the Jacobson Radical of semicrossed products of the disk algebra
    2012
    Co-Authors: Anchalee Khemphet
    Abstract:

    In this thesis, we characterize the Jacobson Radical of the semicrossed product A(D)×α Z+ of the disk algebra by an endomorphism α where α is defined by the composition with a finite Blaschke product φ. Precisely, the Jacobson Radical is the set of those whose 0th Fourier coefficient is identically zero and whose kth Fourier coefficient vanishes on the set of recurrent points of φ. Moreover, if φ is elliptic, i.e., φ has a fixed point in the open unit disc, then the Jacobson Radical coincides with the set of quasinilpotent elements.

Allan P Donsig - One of the best experts on this subject based on the ideXlab platform.

  • the Jacobson Radical for analytic crossed products
    Journal of Functional Analysis, 2001
    Co-Authors: Allan P Donsig, A Katavolos, Antonios Manoussos
    Abstract:

    We characterise the Jacobson Radical of an analytic crossed product C0(X)×φ Z+, answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Jacobson Radical of analytic crossed products C0(X)×φ Zd+. This consists of all elements whose “Fourier coefficients” vanish on the recurrent points of the dynamical system (and the first one is zero). The multidimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.

  • the Jacobson Radical for analytic crossed products
    arXiv: Operator Algebras, 2000
    Co-Authors: Allan P Donsig, A Katavolos, Antonios Manoussos
    Abstract:

    We characterise the (Jacobson) Radical of the analytic crossed product of C_0(X) by the non-negative integers (Z_+), answering a question first raised by Arveson and Josephson in 1969. In fact, we characterise the Radical of analytic crossed products of C_0(X) by (Z_+)^d. The Radical consists of all elements whose `Fourier coefficients' vanish on the recurrent points of the dynamical system (and the first one is zero). The multi-dimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.