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Gu, Caixing
Linear algebra and its applications, 06/2014, Letnik: 451Journal Article
The study of m-isometry elementary operator of length one is initiated by Botelho and Jamison. Several authors have contributed to obtain this result: if the two operator coefficients involved are m-isometries then the elementary operator is m-isometry on the Hilbert–Schmidt operator ideal. In this paper we show that the converse of this result is also true. We also give a necessary and sufficient condition for the generalized derivation to be an m-isometry. The sufficiency follows from results on the sum of m-isometries and nilpotent operators in two recent papers.
