ABSTRACT. Let H b e a bounded finitely connected region in the complex
plane, whose boundary T consists of disjoint, analytic, simple closed curves.
We consider linear bounded operators on a Hilbert space H having Q as
spectral set, and no normal summand with spectrum in I\ For each op-
erator satisfying these properties, we define a weak*-continuous functional
calculus representation 1 : H°°(Q) —• C(H), where H°°(Q,) is the Banach
algebra of bounded analytic functions on Q. An operator is said to be of
class Co if the associated functional calculus has a non-trivial kernel. In
this paper we study operators of class Co, for which we provide a complete
classification into quasisimilarity classes, analogous to the case of the unit
disk.
Key words and phrases. Hardy spaces; Hilbert spaces; Functional Calculus;
Classification; Quasisimilarity; Jordan blocks.
Author address:
DlPARTIMENTO DI MATEMATICA - UNIVERSITA DI MlLANO
VIA SALDINI
50, 20133
MILANO,
ITALY
E-mail address: zucchi@vmi.mat.mat.unimi. i t
Received by the editor December 12, 1994.
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