# ${H}^{\infty}$ functional calculus in real interpolation spaces

Studia Mathematica (1999)

- Volume: 137, Issue: 2, page 161-167
- ISSN: 0039-3223

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topDore, Giovanni. "$H^∞$ functional calculus in real interpolation spaces." Studia Mathematica 137.2 (1999): 161-167. <http://eudml.org/doc/216681>.

@article{Dore1999,

abstract = {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.},

author = {Dore, Giovanni},

journal = {Studia Mathematica},

keywords = {functional calculus; real interpolation; imaginary power; closed densely defined linear operators},

language = {eng},

number = {2},

pages = {161-167},

title = {$H^∞$ functional calculus in real interpolation spaces},

url = {http://eudml.org/doc/216681},

volume = {137},

year = {1999},

}

TY - JOUR

AU - Dore, Giovanni

TI - $H^∞$ functional calculus in real interpolation spaces

JO - Studia Mathematica

PY - 1999

VL - 137

IS - 2

SP - 161

EP - 167

AB - 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.

LA - eng

KW - functional calculus; real interpolation; imaginary power; closed densely defined linear operators

UR - http://eudml.org/doc/216681

ER -

## References

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- [7] A. McIntosh, Operators which have an ${H}_{\infty}$ 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 ${H}_{\infty}$ 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.

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