On an integral of fractional power operators

• Autorzy: Nick Dungey
• Języki publikacji: EN

Abstrakty

EN

For a bounded and sectorial linear operator V in a Banach space, with spectrum in the open unit disc, we study the operator $Ṽ = ∫_{0}^{∞} dα V^{α}$. We show, for example, that Ṽ is sectorial, and asymptotically of type 0. If V has single-point spectrum {0}, then Ṽ is of type 0 with a single-point spectrum, and the operator I-Ṽ satisfies the Ritt resolvent condition. These results generalize an example of Lyubich, who studied the case where V is a classical Volterra operator.

Kategorie tematyczne

• 47A60: Functional calculus
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 117
• Numer: 2
• Strony: 157-164

Daty

wydano

2009

Twórcy

autor

Nick Dungey

• Department of Mathematics, Macquarie University, Sydney, NSW 2109, Australia

Identyfikatory

DOI

10.4064/cm117-2-1