Bulletin of the
Korean Mathematical Society BKMS

This paper concerns the propagation phenomenon of weighted shifts. We here establish the existence of positive real numbers $b$ and $c$ $(1 < b < c )$ such that the recursive weighted shift $W_{1,(1,\sqrt{b},\sqrt{c})^\wedge}$ is quadratically but not cubically hyponormal.

Keywords: weighted shifts, subnormal, $k$-hyponormal, quadratically hyponormal, cubically hyponormal

MSC numbers: Primary 47B20, 47B37