A Fej\'{e}r-type theorem is proved within the framework of $C^*$-algebras associated with certain irreversible algebraic dynamical systems. This makes it possible to strengthen a result on structure relative commutant family generating isometries in boundary quotient.

We provide a general description of realisations of W–algebras in terms of smaller W–algebras and free fields. This is based on the definition of the W–algebra as the commutant of a set of screening charges. This is conjectured to be related to partial gauge-fixings in the Hamiltonian reduction model. Mar 1992 1Email: [email protected]

We present a to following results in the constructive theory of operator algebras. A representation theorem for finite dimensional von Neumann-algebras. A representation theorem for normal functionals. The spectral measure is independent of the choice of the basis of the underlying Hilbert space. Finally, the double commutant theorem for finite von Neumann algebras and for Abelian von Neumann a...

Let T be the C∗-algebra generated by the Toeplitz operators {Tf : f ∈ L∞(B, dv)} on the Bergman space of the unit ball. We show that the essential commutant of T equals {Tg : g ∈ VObdd}+K, where VObdd is the collection of bounded functions of vanishing oscillation on B and K denotes the collection of compact operators on La(B, dv).