Ideals of the Fourier algebra, supports and harmonic operators

We examine the common null spaces of families of HerzSchurmultipliers and apply our results to study jointly harmonic operatorsand their relation with jointly harmonic functionals. We show howan annihilation formula obtained in [1] can be used to give a short proofas well as a generalisation of a result of Neufang and Runde concerningharmonic operators with respect to a normalised positive definite function.We compare the two notions of support of an operator that havebeen studied in the literature and show how one can be expressed interms of the other

Operator algebras from the discrete Heisenberg semigroup

We study reflexivity and structure properties of operator algebras generated by representations of the discrete Heisenberg semi-group. We show that the left regular representation of this semi-group gives rise to a semi-simple reflexive algebra. We exhibit an example of a representation which gives rise to a non-reflexive algebra. En route, we establish reflexivity results for subspaces of H^{\infty}(\bb{T})\otimes\cl B(\cl H)