Operators on Partial Inner Product Spaces: Towards a Spectral Analysis

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• 作者：Jean-Pierre Antoine ; Camillo Trapani
• 关键词：46Cxx ; 47A10 ; 47B37 ; Partial inner product spaces ; lattices of Hilbert spaces ; spectral properties of symmetric operators ; resolvent ; frame multipliers
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：13
• 期：1
• 页码：323-351
• 全文大小：760 KB
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• 作者单位：Jean-Pierre Antoine (1)
  Camillo Trapani (2)
  
  1. Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, 1348, Louvain-la-Neuve, Belgium
  2. Dipartimento di Matematica e Informatica, Università di Palermo, 90123, Palermo, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

Given a Lattice of Hilbert spaces V _J and a symmetric operator A in V _J , in the sense of partial inner product spaces, we define a generalized resolvent for A and study the corresponding spectral properties. In particular, we examine, with help of the KLMN theorem, the question of generalized eigenvalues associated to points of the continuous (Hilbertian) spectrum. We give some examples, including so-called frame multipliers. Mathematics Subject Classification 46Cxx 47A10 47B37