On the Spectral Decomposition of Dichotomous and Bisectorial Operators

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• 作者：Monika Winklmeier ; Christian Wyss
• 关键词：Primary 47A15 ; Secondary 47A10 ; 47A55 ; 47A60 ; 47B44 ; Bisectorial operator ; dichotomous operator ; unbounded projection ; invariant subspace ; p ; subordinate perturbation
• 刊名：Integral Equations and Operator Theory
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：82
• 期：1
• 页码：119-150
• 全文大小：472 KB
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• 作者单位：Monika Winklmeier (1)
  Christian Wyss (2)
  
  1. Departamento de Matem谩ticas, Universidad de los Andes, Cra. 1a No 18A-70, Bogot谩, Colombia
  2. Fachgruppe Mathematik und Informatik, Bergische Universit盲t Wuppertal, Gau脽str. 20, 42097, Wuppertal, Germany
  
• 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

For an unbounded operator S on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on S is the uniform boundedness of the resolvent along the imaginary axis. The projections associated with the invariant subspaces are bounded if S is strictly dichotomous, but may be unbounded in general. Explicit formulas for these projections in terms of resolvent integrals are derived and used to obtain perturbation theorems for dichotomy. All results apply, with certain simplifications, to bisectorial operators.