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1

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

100%

Dore G.

Studia Mathematica

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2001

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tom 145

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nr 1

75-83

EN

Let A be a linear closed one-to-one operator in a complex Banach space X, having dense domain and dense range. If A is of type ω (i.e.the spectrum of A is contained in a sector of angle 2ω, symmetric about the real positive axis, and $||λ(λI - A)^{-1}||$ is bounded outside every larger sector), then A has a bounded $H^{∞}$ functional calculus in the real interpolation spaces between X and the intersection of the domain and the range of the operator itself.

2

$H^∞$ functional calculus in real interpolation spaces

100%

Dore G.

Studia Mathematica

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1999

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tom 137

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nr 2

161-167

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.

3

$H^{∞}$ functional calculus for sectorial and bisectorial operators

63%

Dore G., Venni A.

Studia Mathematica

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2005

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tom 166

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nr 3

221-241

EN

We give a concise exposition of the basic theory of $H^{∞}$ functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator $f(T₁,...,T_{N})$ when f is an R-bounded operator-valued holomorphic function.

Ograniczanie wyników

3 Studia Mathematica

3 Dore G.

1 Venni A.

1 2005

1 2001

1 1999

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

$H^∞$ functional calculus in real interpolation spaces

$H^{∞}$ functional calculus for sectorial and bisectorial operators