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.
Isometric $N$-Jordan operator, nilpotent, weighted shift operator
YARMAHMOODI, SAEED and HEDAYATIAN, KARIM
"Isometric $N$-Jordan weighted shift operators,"
Turkish Journal of Mathematics: Vol. 40:
5, Article 17.
Available at: https://journals.tubitak.gov.tr/math/vol40/iss5/17