Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589913 | Journal of Functional Analysis | 2015 | 20 Pages |
Abstract
The weak operator topology closed operator algebra on L2(R)L2(R) generated by the one-parameter semigroups for translation, dilation and multiplication by eiλx,λ≥0eiλx,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, AphAph, is antisymmetric in the sense that Aph∩Aph⁎=CI, it has a nonzero proper weakly closed ideal generated by the finite-rank operators, and its unitary automorphism group is RR. Furthermore, the 8 choices of semigroup triples provide 2 unitary equivalence classes of operator algebras, with AphAph and Aph⁎ being chiral representatives.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
E. Kastis, S.C. Power,