The 3-Isometric Lifting Theorem

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• 作者：Scott McCullough ; Benjamin Russo
• 关键词：Dilation theory ; 3 ; symmetric operators ; 3 ; isometric operators ; non ; normal spectral theory ; complete positivity ; Wiener–Hopf factorization
• 刊名：Integral Equations and Operator Theory
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：84
• 期：1
• 页码：69-87
• 全文大小：586 KB
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• 作者单位：Scott McCullough (1)
  Benjamin Russo (1)
  
  1. Department of Mathematics, University of Florida, Gainesville, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989

文摘

An operator T on Hilbert space is a 3-isometry if \({T^{*n}T^{n}= I +n B_1 +n^{2} B_2}\) is quadratic in n. An operator J is a Jordan operator if J = U + N where U is unitary, N 2 = 0 and U and N commute. If T is a 3-isometry and \({c > 0,}\) then \({I-c^{-2} B_{2} + sB_{1} + s^{2}B_2}\) is positive semidefinite for all real s if and only if it is the restriction 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.