$H^∞$ functional calculus in real interpolation spaces

• Autorzy: Giovanni Dore
• Języki publikacji: EN

Abstrakty

EN

Let A be a linear closed densely defined operator in a complex Banach space X. If A is of type ω (i.e. the spectrum of A is contained in a sector of angle 2ω, symmetric around the real positive axis, and $∥λ(λ I - A)^{-1}∥$ is bounded outside every larger sector) and has a bounded inverse, then A has a bounded $H^∞$ functional calculus in the real interpolation spaces between X and the domain of the operator itself.

Kategorie tematyczne

• 46B70: Interpolation between normed linear spaces
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 137
• Numer: 2
• Strony: 161-167

Daty

wydano

1999

otrzymano

1998-07-10

poprawiono

1999-07-30

Twórcy

autor

Giovanni Dore

• Dipartimento di Matematica, Università di Bologna, Piazza di Porta, S. Donato 5, 40127 Bologna, Italy

Bibliografia

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• [7] A. McIntosh, Operators which have an $H_∞$ functional calculus, in: Miniconference on Operator Theory and Partial Differential Equations (Macquarie University, Ryde, N.S.W., September 8-10, 1986), B. Jefferies, A. McIntosh and W. Ricker (eds.), Proc. Centre Math. Anal. Austral. Nat. Univ. 14, Austral. Nat. Univ., Canberra, 1986, 210-231.
• [8] A. McIntosh and A. Yagi, Operators of type ω without a bounded $H_∞$ functional calculus, in: Miniconference on Operators in Analysis (Macquarie University, Sydney, N.S.W., September 25-27, 1989), I. Doust, B. Jefferies, C. Li and A. McIntosh (eds.), Proc. Centre Math. Anal. Austral. Nat. Univ. 24, Austral. Nat. Univ., Canberra, 1989, 159-172.
• [9] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978.