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S C Power - One of the best experts on this subject based on the ideXlab platform.

  • the Operator algebra generated by the translation dilation and multiplication semigroups
    Journal of Functional Analysis, 2015
    Co-Authors: Eleftherios Kastis, S C Power
    Abstract:

    Abstract The weak Operator topology Closed Operator algebra on L 2 ( R ) generated by the one-parameter semigroups for translation, dilation and multiplication by e i λ x , λ ≥ 0 , is shown to be a reflexive Operator algebra, in the sense of Halmos, with invariant subspace lattice equal to a binest. This triple semigroup algebra, A p h , is antisymmetric in the sense that A ph ∩ A p h ⁎ = C I , it has a nonzero proper weakly Closed ideal generated by the finite-rank Operators, and its unitary automorphism group is R . Furthermore, the 8 choices of semigroup triples provide 2 unitary equivalence classes of Operator algebras, with A ph and A p h ⁎ being chiral representatives.

  • the Operator algebra generated by the translation dilation and multiplication semigroups
    arXiv: Operator Algebras, 2014
    Co-Authors: Eleftherios Kastis, S C Power
    Abstract:

    The weak Operator topology Closed Operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive Operator algebra, in the sense of Halmos, with invariant subspace lattice equal to a binest. This triple semigroup algebra, $A_{ph}$, is antisymmetric in the sense that $A_{ph} \cap A_{ph}^*= CI$, it has a nonzero proper weakly Closed ideal generated by the finite-rank Operators, and its unitary automorphism group is $R$. Furthermore, the 8 choices of semigroup triples provide 2 unitary equivalence classes of Operator algebras, with $A_{ph}$ and $A_{ph}^*$ being chiral representatives.

Eleftherios Kastis - One of the best experts on this subject based on the ideXlab platform.

  • the Operator algebra generated by the translation dilation and multiplication semigroups
    Journal of Functional Analysis, 2015
    Co-Authors: Eleftherios Kastis, S C Power
    Abstract:

    Abstract The weak Operator topology Closed Operator algebra on L 2 ( R ) generated by the one-parameter semigroups for translation, dilation and multiplication by e i λ x , λ ≥ 0 , is shown to be a reflexive Operator algebra, in the sense of Halmos, with invariant subspace lattice equal to a binest. This triple semigroup algebra, A p h , is antisymmetric in the sense that A ph ∩ A p h ⁎ = C I , it has a nonzero proper weakly Closed ideal generated by the finite-rank Operators, and its unitary automorphism group is R . Furthermore, the 8 choices of semigroup triples provide 2 unitary equivalence classes of Operator algebras, with A ph and A p h ⁎ being chiral representatives.

  • the Operator algebra generated by the translation dilation and multiplication semigroups
    arXiv: Operator Algebras, 2014
    Co-Authors: Eleftherios Kastis, S C Power
    Abstract:

    The weak Operator topology Closed Operator algebra on $L^2(R)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $exp(i\lambda x), \lambda \geq 0$, is shown to be a reflexive Operator algebra, in the sense of Halmos, with invariant subspace lattice equal to a binest. This triple semigroup algebra, $A_{ph}$, is antisymmetric in the sense that $A_{ph} \cap A_{ph}^*= CI$, it has a nonzero proper weakly Closed ideal generated by the finite-rank Operators, and its unitary automorphism group is $R$. Furthermore, the 8 choices of semigroup triples provide 2 unitary equivalence classes of Operator algebras, with $A_{ph}$ and $A_{ph}^*$ being chiral representatives.

Hansolav Tylli - One of the best experts on this subject based on the ideXlab platform.

  • duality of the distance to Closed Operator ideals
    Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2003
    Co-Authors: Hansolav Tylli
    Abstract:

    Special Operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist( S *, I ( F *, E *)) and S ↦ dist( S , I *( E , F )) are uniformly comparable in each space L ( E , F ) of bounded linear Operators. Here, I *( E , F ) = { S ∈ L ( E , F ) : S * ∈ I ( F *, E *)} stands for the adjoint ideal of the Closed Operator ideal I for Banach spaces E and F . Counterexamples are obtained for many classical surjective or injective Banach Operator ideals I by solving two resulting ‘asymmetry’ problems for these Operator-ideal APs.

Anton Martinez - One of the best experts on this subject based on the ideXlab platform.

Fernando Cobos - One of the best experts on this subject based on the ideXlab platform.