On the Cesáro Operator in Weighted `-sequence Spaces and the Generalized Concept of Normality

The weighted Cesáro operator Ch in ` (h)-spaces is investigated in terms of several concepts of normality, where h denotes a positive discrete measure on N0. We classify exactly those h for which Ch is hyponormal. Two examples related to the Haar measures of orthogonal polynomials are discussed. We show that the Cesáro operator is not always paranormal. Furthermore, we prove that the Cesáro operator is not quasinormal for any choice of h. Department of Mathematics, M12, Technische Universität München, Boltzmannstr. 3, 85748 Garching, Germany. E-mail address: [email protected] Date: Received: 15 October 2012; Accepted: 6 November 2012. 2010 Mathematics Subject Classification. Primary 47B37; Secondary 47B20, 33D45.