Tensor products of subspace lattices and rank one density

We show that, if M is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, L is a commutative subspace lattice and P is the lattice of all projections on a separable Hilbert space, then L⊗M⊗P is reflexive. If M is moreover an atomic Boolean subspace lattice while L is any subspace lattice, we provide a concrete lattice theoretic description of L⊗M in terms of projection valued functions defined on the set of atoms of M . As a consequence, we show that the Lattice Tensor Product Formula holds for AlgM and any other reflexive operator algebra and give several further corollaries of these results.

Authorizing a tradition: Theory, criticism and (self-) canonization in French Caribbean writing

As critics have noted, Antillean literature has developed in tandem with a strong (self-) critical and theoretical body of work. The various attempts to theorize Antillean identity (négritude, antillanité, créolité) have been controversial and divisive, and the literary scene has been characterized as explosive, incestuous and self-referential. Yet writers aligned with, or opposed to, a given theory often have superior visibility. Meanwhile writers who claim to operate outside the boundaries of theory, such as Maryse Condé, are often canny theoretical operators who, from prestigious academic or cultural positions, manipulate readers’ responses and their own self-image through criticism. While recent polemics have helped to raise the critical stock of the islands generally, they have particularly enhanced the cultural capital of Chamoiseau and Condé, whose literary antagonism is in fact mutually sustaining. Both writers, through a strong awareness of (and contribution to) the critical field in which their work is read, position themselves as canonical authors.