Geodesic
$H^{\infty }$ functional calculus for sectorial and bisectorial operators
Giovanni Dore1 ; Alberto Venni1
1 Dipartimento di Matematica Piazza di Porta San Donato, 5 I-40127 Bologna, Italy
Studia Mathematica, Tome 166 (2005) no. 3, pp. 221-241 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We give a concise exposition of the basic theory of $H^\infty$ 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 $f(T_1,\ldots,T_N)$ when $f$ is an R-bounded operator-valued holomorphic function.
DOI : 10.4064/sm166-3-2
Keywords: concise exposition basic theory infty functional calculus n tuples sectorial bisectorial operators respect operator valued functions moreover restate prove setting result kalton weis about boundedness operator ldots r bounded operator valued holomorphic function

Giovanni Dore 1 ; Alberto Venni 1

1 Dipartimento di Matematica Piazza di Porta San Donato, 5 I-40127 Bologna, Italy 
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Giovanni Dore; Alberto Venni. $H^{\infty }$ functional calculus for sectorial
 and bisectorial operators. Studia Mathematica, Tome 166 (2005) no. 3, pp. 221-241. doi: 10.4064/sm166-3-2

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