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Abstract and Applied Analysis
Volume 2014, Article ID 745479, 6 pages
Research Article

Perturbation of -Isometries by Nilpotent Operators

1Departamento de Análisis Matemático, Universidad de La Laguna, La Laguna, 38271 Tenerife, Spain
2Mathematical Institute, Czech Academy of Sciences, 115 67 Prague, Czech Republic

Received 8 April 2014; Accepted 18 July 2014; Published 9 September 2014

Academic Editor: Feyzi Başar

Copyright © 2014 Teresa Bermúdez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove that if is an -isometry on a Hilbert space and an -nilpotent operator commuting with , then is a -isometry. Moreover, we show that a similar result for -isometries on Banach spaces is not true.