Geodesic
Normal and quasinormal weighted composition operators
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 275-279

Voir la notice de l'article provenant de la source Cambridge University Press

In their paper [1], Campbell and Jamison attempted to give necessary and sufficient conditions for a weighted composition operator on an L2 space to be normal, and to be quasinormal. Those conditions, specifically Theorems I and II of that paper, are not valid (see [2] for precise comments on the other results in that paper). In this paper we present a counterexample to those theorems and state and prove characterizations of quasinormality (Theorem 1 below) and normality (Theorem 2 and Corollary 3 below). We also discuss additional examples and information concerning normal weighted composition operators which contribute to the further understanding of this class. 
Campbell, James T.; Embry-Wardrop, Mary; Fleming, Richard J.; Narayan, S. K. Normal and quasinormal weighted composition operators. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 275-279. doi: 10.1017/S0017089500008338
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[1] 1.Campbell, J. and Jamison, J., On some classes of weighted composition operators, Glasgow Math. J. 32 (1990), 87–94. Google Scholar | DOI

[2] 2.Campbell, J. and Jamison, J., Errata to: On some classes of weighted composition operators, Glasgow Math. J. 32 (1990), 261–263. Google Scholar | DOI

[3] 3.Foguel, S., The ergodic theory of Markov processes, Math. Studies No. 21 (Van Nostrand Reinhold, New York, 1969). Google Scholar

[4] 4.Lambert, A., Hyponormal composition operators, Bull. London Math. Soc. 18 (1986), 395–400. Google Scholar | DOI

[5] 5.Whitley, R., Normal and quasinormal composition operators, Proc. Amer. Math. Soc. 70 (1978), 114–118. Google Scholar | DOI

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