Some Remarks On Essentially Normal Submodules

Mathematics – Functional Analysis

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

Given a *-homomorphism $\sigma: C(M)\to \mathscr{L}(\mathcal{H})$ on a Hilbert space $\mathcal{H}$ for a compact metric space $M$, a projection $P$ onto a subspace $\mathcal{P}$ in $\mathcal{H}$ is said to be essentially normal relative to $\sigma$ if $[\sigma(\varphi),P]\in \mathcal{K}$ for $\varphi\in C(M)$, where $\mathcal{K}$ is the ideal of compact operators on $\mathcal{H}$. In this note we consider two notions of span for essentially normal projections $P$ and $Q$, and investigate when they are also essentially normal. First, we show the representation theorem for two projections, and relate these results to Arveson's conjecture for the closure of homogenous polynomial ideals on the Drury-Arveson space. Finally, we consider the relation between the relative position of two essentially normal projections and the $K$ homology elements defined for them.

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

Some Remarks On Essentially Normal Submodules 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 Some Remarks On Essentially Normal Submodules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some Remarks On Essentially Normal Submodules will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-354657

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