2013/06/23 by Scott McCullough, McCullough, Scott, Benjamin Russo +1
Mathematics · #47B38 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #[2010] 47A20 (Primary) 47B37 #math.FA #msc:47A20 #msc:47B37 #msc:47B38
paper · pdf · doi:10.48550/arxiv.1306.5444
arxiv created 2013/06/23 · arxiv updated 2013/06/25
An operator T on Hilbert space is a 3-isometry if there exists operators B and D such that (T*)n Tn = I+nB +n2 D. An operator J is a Jordan operator if it the sum of a unitary U and nilpotent N of order two which commute. If T is a 3-isometry and c>0, then I-c-2 D + sB + s2D is positive semidefinite for all real s if and only if T is the restriction to an invariant subspace of a Jordan operator J=U+N with the norm of N at most c. As a corollary, an analogous result for 3-symmetric operators, due to Helton and Agler, is recovered.