Propagation phenomena for 𝑘-hyponormal matricial weighted shifts

Source abstract

We study matricial subnormal and matricial k k -hyponormal completion problems. We extend J. Stampfli’s Theorem on flat propagation of subnormal scalar weighted shifts to the case of 2 2 -hyponormal matricial weighted shifts. On the one hand, we fill the missing part in N. Ivanovski’s theorem concerning inner propagation, and on the other hand, we extend R.E. Curto’s theorem on propagation phenomena for scalar weighted shifts to the case of 2 2 -hyponormal matricial weighted shifts. As an added feature, some of the proofs we present for the matricial case are new in the scalar case.