Let T be the Toeplitz algebra on the Bergman space La(B, dv) of the unit ball in C. We show that the image of T in the Calkin algebra satisfies the double commutant relation: π(T ) = {π(T )}′′. This is a surprising result, for it is the opposite of what happens in the Hardy-space case [16,17].

It was observed by Gilfeather, Hopenwasser, and Larson in [1] that Tomita's commutation formula for tensor products of von Neumann algebras can be rewritten in a way that makes sense for tensor products of arbitrary reflexive algebras. The tensor product problem for reflexive algebras is to decide for which pairs of reflexive algebras this tensor product formula is valid. Recall that a subalgeb...

We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II(1), factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

Defining the WBCn algebras as the commutant of certain screening charges a special form for the classical generators is obtained which does not change under quantisation. This enables us to give explicitly the first few generators in a compact form for arbitrary WBCn algebras.

We provide a complete classification up to conjugacy of the binary shifts of commutant index 2 on the hyperfinite II(1) factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.

In this paper, we give an explicit description of the commutant algebras for vector fields Lie algebras Wn in their representations on Wm×n, m 6 n, which arises from the tensor product Nm CoindF n, for the basis field F of characteristic 0. The result is some analogue of Weyl’s classical reciprocity.