Tensor products of subspace lattices and rank one density

Details Tensor products of subspace lattices and rank one density Tensor products of subspace lattices and rank one density

2012-03-28

arxiv.org/abs/1203.6391v3

Mathematics

Functional Analysis

15 pages

Scientific paper

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 infinite dimensional Hilbert space, then the lattice $L\otimes M\otimes P$ 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 $L\otimes M$ 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 $\Alg M$ and any other reflexive operator algebra and give several further corollaries of these results.

Affiliated with

Also associated with

No associations

Rating

Tensor products of subspace lattices and rank one density does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Tensor products of subspace lattices and rank one density, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tensor products of subspace lattices and rank one density will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-56907