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Journal d’Analyse Mathématique

, Volume 98, Issue 1, pp 221–247 | Cite as

Operators with smooth functional calculi

  • Mats AnderssonEmail author
  • H⇘kan Samuelsson
  • Sebastian Sandberg
Article

Abstract

We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, which contains all operators of Helffer-Sjöstrand type and is closed under the action of smooth proper mappings. Moreover, the class is closed under tensor product of commuting operators. In general, and operator in this class has no resolvent in the usual sense, so the spectrum must be defined in terms of the functional calculus. We also consider invariant subspaces and spectral decompositions.

Keywords

Tensor Product Compact Support Spectral Decomposition Functional Calculus Continuous Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University Magnes Press 2006

Authors and Affiliations

  • Mats Andersson
    • 1
    Email author
  • H⇘kan Samuelsson
    • 1
  • Sebastian Sandberg
    • 1
  1. 1.Department of MathematicsChalmers University of Technology and the University of GöteborgGöteborgSweden

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