PORTUGALIAE MATHEMATICA Vol. 62, No. 2, pp. 185191 (2005) 

Every nilpotent operator fails to determine the complete norm topologyMourad Oudghiri and Mohamed ZohryDepartment of Mathematics, University Abdelmalek Essaadi,BP 2121, Tetouan  MOROCCO Email: mourad_oudghiri@hotmail.com , zohry@fst.ac.ma Abstract: We show that every nilpotent operator $T$, on an infinitedimensional Banach space $X$, provides a decomposition of $X$ into a direct sum of a finite number of subspaces with sufficiently connections. Finally we construct a complete norm on $X$ that makes $T$ continuous and not equivalent to the original norm on $X$. Keywords: uniqueness of complete norm topology; nilpotent operator. Classification (MSC2000): 47A53, 47A68, 46B04. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2005 Sociedade Portuguesa de Matemática
