Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 62, No. 2, pp. 185-191 (2005)

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Every nilpotent operator fails to determine the complete norm topology

Mourad Oudghiri and Mohamed Zohry

Department of Mathematics, University Abdelmalek Essaadi,
BP 2121, Tetouan -- MOROCCO
E-mail: mourad_oudghiri@hotmail.com , zohry@fst.ac.ma

Abstract: We show that every nilpotent operator $T$, on an infinite-dimensional 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.

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Electronic version published on: 7 Mar 2008.

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