H ∞ functional calculus in real interpolation spaces

Giovanni Dore

Studia Mathematica (1999)

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

Abstract

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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.

How to cite

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Dore, 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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  1. [1] K. N. Boyadzhiev and R. J. deLaubenfels, H ∞ functional calculus for perturbations of generators of holomorphic semigroups, Houston J. Math. 17 (1991), 131-147. Zbl0738.47018
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  3. [3] M. Cowling, I. Doust, A. McIntosh and A. Yagi, Banach space operators with a bounded H ∞ functional calculus, J. Austral. Math. Soc. Ser. A 60 (1996), 51-89. Zbl0853.47010
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  7. [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. [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. [9] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. 

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