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

Cowen, Carl C.

Indiana Univ. Math. J. 33, 305-318 (1984).

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

MSC:

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

Keywords:

strongly continuous semigroup of subnormal composition operators; subnormal Volterra integral operator; discrete Cesàro operator

Citations:

Zbl 0235.46022