Fresh Examples of Hyponormal Terraced Matrices with Transcendental Entries

Abstract

This note calls attention to an alternative version of the main result from [4], which can be used together with Maclaurin series expansions and trigonometric identities to show that the terraced matrices generated by the sequences $\{\ln (1+1/(n+1)):n\ge 0\}$, $\{\tan (1/(n+2)):n\ge 0\}$, and $\{\sinh (1/(n+2)):n\ge 0\}$ are hyponormal operators on ${\ell }^2$. Along the way it is also shown that the matrix generated by $\{\tan (1/(n+1)):n\ge 0\}$ is not a hyponormal operator on ${\ell }^2$.

6 pages