Projection decomposition in multiplier algebras

Mathematics – Operator Algebras

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

To appear in Mathematische Annalen

Scientific paper

10.1007/s00208-011-0649-0

In this paper we present new structural information about the multiplier algebra Mult (A) of a sigma-unital purely infinite simple C*-algebra A, by characterizing the positive elements a in Mult(A) that are strict sums of projections belonging to A. If a is not in A and is not a projection, then the necessary and sufficient condition for a to be a strict sum of projections belonging to A is that the norm ||a||>1 and that the essential norm ||a||_ess >=1. Based on a generalization of the Perera-Rordam weak divisibility of separable simple C*-algebras of real rank zero to all sigma-unital simple C*-algebras of real rank zero, we show that every positive element of A with norm greater than 1 can be approximated by finite sums of projections. Based on block tri-diagonal approximations, we decompose any positive element a in Mult(A) with ||a||>1 and ||a||_ess >=1 into a strictly converging sum of positive elements in A with norm greater than 1.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

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

Rate now

     

Profile ID: LFWR-SCP-O-498405

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.