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A local directional growth estimate of the resolvent norm

Publikation: Working paperForskning

  • Horia Cornean, Institut for Matematiske Fag, Aalborg Universitet, Danmark
  • Henrik Garde
  • Arne Jensen, Institut for Matematiske Fag, Aalborg Universitet, Danmark
  • Hans Konrad Knörr, Institut for Matematiske Fag, Aalborg Universitet
We study the resolvent norm of a certain class of closed linear operators on a Hilbert space, including unbounded operators with compact resolvent. It is shown that for any point in the resolvent set there exist directions in which the norm grows at least quadratically with the distance from this point. This provides a new proof not using the maximum principle that the resolvent norm of the considered class cannot have local maxima. Finally, we give new criteria for the existence of local non-degenerate minima of the resolvent norm and provide examples of (un)bounded non-normal operators having this property.
OriginalsprogEngelsk
StatusUnder udarbejdelse - 2018
Eksternt udgivetJa

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