Isometric $N$-Jordan weighted shift operators

Authors: SAEED YARMAHMOODI, KARIM HEDAYATIAN

Abstract: A bounded linear operator $T$ on a Hilbert space is an isometric $N$-Jordan operator if it can be written as $A+Q$, where $A$ is an isometry and $Q$ is a nilpotent of order $N$ such that $AQ= QA$. In this paper, we will show that the only isometric $N$-Jordan weighted shift operators are isometries. This answers a question recently raised.

Keywords: Isometric $N$-Jordan operator, nilpotent, weighted shift operator

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