Propagation phenomena for hyponormal 2-variable weighted shifts

Details Propagation phenomena for hyponormal 2-variable weighted shifts Propagation phenomena for hyponormal 2-variable weighted shifts

2006-10-28

arxiv.org/abs/math/0610889v1

Mathematics

Functional Analysis

Scientific paper

We study the class of hyponormal 2-variable weighted shifts with two consecutive equal weights in the weight sequence of one of the coordinate operators. We show that under natural assumptions on the coordinate operators, the presence of consecutive equal weights leads to horizontal or vertical flatness, in a way that resembles the situation for 1-variable weighted shifts. In 1-variable, it is well known that flat weighted shifts are necessarily subnormal (with finitely atomic Berger measures). By contrast, we exhibit a large collection of flat (i.e., horizontally and vertically flat) 2-variable weighted shifts which are hyponormal but not subnormal. Moreover we completely characterize the hyponormality and subnormality of symmetrically flat contractive 2-variable weighted shifts.

Affiliated with

Also associated with

No associations

Rating

Propagation phenomena for hyponormal 2-variable weighted shifts 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 Propagation phenomena for hyponormal 2-variable weighted shifts, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Propagation phenomena for hyponormal 2-variable weighted shifts will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-652102