Home > Research > Publications & Outputs > The operator algebra generated by the translati...

Electronic data

  • kastispower1

    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 269, 2015 DOI: 10.1016/j.jfa.2015.08.005

    Accepted author manuscript, 354 KB, PDF document

    Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License

Links

Text available via DOI:

View graph of relations

The operator algebra generated by the translation, dilation and multiplication semigroups

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>27/09/2015
<mark>Journal</mark>Journal of Functional Analysis
Volume269
Number of pages19
Pages (from-to)3316-3335
Publication StatusPublished
Early online date24/08/15
<mark>Original language</mark>English

Abstract

The weak operator topology closed operator algebra on $L^2(\bR)$ generated by the one-parameter semigroups for translation, dilation and multiplication by $e^{i\lambda x}, \lambda \geq 0,$ 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 $\A_{ph}\cap \A_{ph}^*=\bC I$, it
has a nonzero proper weakly closed ideal generated by the finite-rank operators, and its unitary automorphism group is $\bR$. Furthermore, the $8$ choices of semigroup triples provide $2$ unitary equivalence classes of operator algebras, with $\A_{ph}$ and $\A_{ph}^*$ being chiral representatives.



Bibliographic note

This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Functional Analysis, 269, 2015 DOI: 10.1016/j.jfa.2015.08.005