TRO equivalent algebras

Details TRO equivalent algebras TRO equivalent algebras

2006-07-20

arxiv.org/abs/math/0607488v3

Mathematics

Operator Algebras

This article has been accepted for publication to the journal Houston of Mathematics. The referee of the article found a gap i

Scientific paper

In this work we study a new equivalence relation between w* closed algebras of operators on Hilbert spaces. The algebras A and B are called TRO equivalent if there exists a ternary ring of operators M (i.e. MM*M\subset M) such that A is the w*-closed span of M*BM and B is the w*-closed span of MAM*. We prove that two reflexive algebras are TRO equivalent if and only if there exists a * isomorphism between the commutants of their diagonals mapping the invariant projection lattice of the first algebra onto the lattice of the second one. We explore some consequences of TRO equivalence for CSL algebras. We also prove that TRO equivalence is stronger than "spatial Morita equivalence". Two CSL algebras are "spatially Morita equivalent" if and only if their lattices are isomorphic. In this case if one of them is synthetic then so is the other.

Affiliated with

Also associated with

No associations

Rating

TRO equivalent algebras 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 TRO equivalent algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and TRO equivalent algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-79701