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

Giovanni Dore¹

¹ Dipartimento di Matematica Universita di Bologna Piazza di Porta S. Donato 5 40127 Bologna, Italy

Studia Mathematica, Tome 145 (2001) no. 1, pp. 75-83

Résumé

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 $\omega $ (i.e.the spectrum of $A$ is contained in a sector of angle $2\omega $, symmetric about the real positive axis, and $\| \lambda (\lambda I - A)^{-1}\| $ is bounded outside every larger sector), then $A$ has a bounded $H^\infty $ functional calculus in the real interpolation spaces between $X$ and the intersection of the domain and the range of the operator itself.

Détail

DOI : 10.4064/sm145-1-5

Keywords: linear closed one to one operator complex banach space having dense domain dense range type omega spectrum contained sector angle omega symmetric about real positive axis lambda lambda bounded outside every larger sector has bounded infty functional calculus real interpolation spaces between intersection domain range operator itself