Instytut Matematyczny Polskiej Akademii Nauk / pl / Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

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.