Subnormality of the Cesàro operator and a semigroup of composition operators. (English) Zbl 0557.47018

A strongly continuous semigroup of subnormal composition operators on \(H^ 2\) of the upper half plane is constructed and investigated. It is shown to be unitarily equivalent to the semigroup of operators of multiplication by \(e^{-\lambda \zeta}\) on a space of analytic functions on the right half plane. This yields a subnormal Volterra integral operator, which is unitarily equivalent to the discrete Cesàro operator. Compared with the subnormality proof for the Cesàro operator achieved by T. L. Kriete and D. Trutt [Am. J. Math. 93, 215- 225 (1971; Zbl 0235.46022)] the measure involved here can be handled more directly. The equivalence of these two different representations of the Cesàro operator is indicated.
Reviewer: G.Garske


47B20 Subnormal operators, hyponormal operators, etc.
47D03 Groups and semigroups of linear operators
47B38 Linear operators on function spaces (general)


Zbl 0235.46022
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