 

Adam H. Fuller and David R. Pitts
Isomorphisms of lattices of Buresclosed bimodules over Cartan MASAs view print


Published: 
October 18, 2013

Keywords: 
Bimodule, Cartan MASA 
Subject: 
Primary 46L10, Secondary 46L51 


Abstract
For i=1,2, let (M_{i},D_{i}) be pairs consisting of
a Cartan MASA D_{i} in a von Neumann algebra M_{i}, let
atom(D_{i}) be the set of atoms of D_{i}, and let S_{i} be the
lattice of Buresclosed D_{i} bimodules in M_{i}. We show that when
M_{i} have separable preduals, there is a lattice isomorphism between
S_{1} and S_{2} if and only if the sets
{(Q_{1}, Q_{2})∈ atom(D_{i})× atom(D_{i}): Q_{1}M_{i}Q_{2}≠ (0)}
have the same
cardinality. In particular, when D_{i} is nonatomic, S_{i} is
isomorphic to the lattice of projections in L^{∞}([0,1],m) where
m is Lebesgue measure, regardless of the isomorphism classes of
M_{1} and M_{2}.


Author information
Adam H. Fuller:
Dept. of Mathematics, University of NebraskaLincoln, Lincoln, NE, 685880130
afuller7@math.unl.edu
David R. Pitts:
Dept. of Mathematics, University of NebraskaLincoln, Lincoln, NE, 685880130
dpitts2@math.unl.edu

