# zbMATH — the first resource for mathematics

Operators of type $$\omega$$ without a bounded $$H_{\infty}$$ functional calculus. (English) Zbl 0709.47016
Miniconference on operators in analysis, Proc. Miniconf., Sydney/Australia 1989, Proc. Cent. Math. Anal. Aust. Natl. Univ. 24, 159-172 (1990).
[For the entire collection see Zbl 0699.00025.]
A. McIntosh [Proc. Cent. Math. Anal. Aust. Natl. Univ. 14, 210-231 (1990; Zbl 0634.47016)] gave several conditions equivalent to a closed operator of type $$\omega$$ in a Hilbert space having a bounded $$H_{\infty}$$ functional calculus.
The authors construct several examples of operators of type $$\omega$$ which do not satisfy these conditions. Moreover, they show that every operator of type $$\omega$$ does have a bounded $$H_{\infty}$$ functional calculus if it is considered as acting in a Hilbert space obtained by a suitable renorming of the initial one.
Reviewer: M.Gonzalez

##### MSC:
 47A60 Functional calculus for linear operators